# Recent questions tagged permutation-combination

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1
A four-digit number is formed by using only the digits $1, 2$ and $3$ such that both $2$ and $3$ appear at least once. The number of all such four-digit numbers is
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2
The number of ways of distributing $15$ identical balloons, $6$ identical pencils and $3$ identical erasers among $3$ children, such that each child gets at least four balloons and one pencil, is
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3
The number of groups of three or more distinct numbers that can be chosen from $1, 2, 3, 4, 5, 6, 7,$ and $8$ so that the groups always include $3$ and $5,$ while $7$ and $8$ are never included together is
4
How many $4$-digit numbers, each greater than $1000$ and each having all four digits distinct, are there with $7$ coming before $3.$
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5
How many $3-$digit numbers are there, for which the product of their digits is more than $2$ but less than $7$?
6
In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together? $10080$ $4989600$ $120960$ None of the options
7
What is the maximum number of the handshakes that can happen in the room with $5$ people in it? $15$ $10$ $6$ $5$
8
In how many different ways can the letters of the word ‘CORPORATION’ be arranged so that the vowels always come together? $810$ $1440$ $2880$ $50400$
9
In a big farm in Wisconsin, there are only hens and cows. When the owner counted the heads of the stock in the farm, the number summed up to $200$, while counting the number of legs, the number summed up to $540$. How many more hens were there in the farm ? Assume each cow had $4$ legs and each hen had $2$ legs. $70$ $120$ $60$ $130$
10
There are $6$ boxes numbered $1,2$,$\dots$,$6$. Each box is to be filled up either with a red or a green ball in such a way that at least $1$ box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is : $5$ $21$ $33$ $60$
11
In a tournament, there are $43$ junior level and $51$ senior level participants. Each pair of juniors play one match. Each pair of seniors play one match. There is no junior versus senior match. The number of girl versus girl matches in junior level is $153$, while the number of boy versus boy matches in senior level is $276$. The number of matches a boy plays against a girl is _________
12
How many numbers with two or more digits can be formed with the digits $1,2,3,4,5,6,7,8,9$, so that in every such number, each digit is used at most once and the digits appear in the ascending order?
13
How many four digits number, which are divisible by $6$ , can be formed using the digits $0,2,3,4,6$ such that no digit is used more than once and $0$ does not occur in the left-most positions? $49$ $48$ $50$ $52$
1 vote
14
In how many ways can $8$ identical pens be distributed among Amal, Bimal, Kamal so that Amal gets at least $1$ pen, Bimal gets a least $2$ pens, and Kamal gets a least $3$ pens? $5$ $6$ $7$ $8$
1 vote
15
In how many ways can $7$ identical erasers be distributed among $4$ kids in such a way that each kid gets at least one eraser but nobody gets more than $3$ erasers? $16$ $20$ $14$ $15$
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16
A man has $9$ friends: $4$ boys and $5$ girls. In how many ways can he invite them, if there have to be exactly $3$ girls in the invitees ________
17
There are $12$ towns grouped into four zones with three towns per zone. It is intended to connect the towns with telephone lines such that every two towns are connected with three direct lines if they belong to the same zone, and with only one direct line otherwise. How many direct telephone lines are required? $72$ $90$ $96$ $144$
18
Rajat draws a $10\times10$ grid on the ground such that there are $100$ identical squares numbered $1\:\text{to}\:100$. If he has to place two identical stones on any two separate squares in the grid, how many distinct ways are possible? $2475$ $4950$ $9900$ $1000$
19
Letters of the word ATTRACT are written on cards and are kept on a table. Manish is asked to lift three cards at a time, write all possible combinations of the three letters on a piece of paper and then replace the three cards. The exercise ends when all possible combinations of ... list, which look the same when seen in a mirror. How many words is he left with? $40$ $20$ $30$ None of these
20
In a factory making radioactive substances, it was considered that the three cubes of uranium together are hazardous. So the company authorities decided to have the stack of uranium interspersed with lead cubes. But there is a new worker in a company who does not know the rule. So he ... he wanted. What is the number of hazardous combinations of uranium in a stack of $5?$ $3$ $7$ $8$ $10$
21
An intelligence agency forms a code of two distinct digits selected from $0, 1, 2, \dots 9$ such that the first digit of the code is nonzero. The code, handwritten on a slip, can however potentially create confusion, when read upside down – for example, the code $91$ may appear as $16.$ How many codes are there for which no such confusion can arise? $80$ $78$ $71$ $69$
22
There are $12$ towns grouped into four zones with three towns per zone. It is intended to connect the towns with telephone lines such that every two towns are connected with three direct lines if they belong to the same zone, and with only one direct line otherwise. How many direct telephone lines are required? $72$ $90$ $96$ $144$
23
Answer the questions on the basis of the information given below. A string of three English letters is formed as per the following rules The first letter is any vowel. The second letter is $m, n$ or $p$. If the second letter is $m,$ then the third letter is any vowel which ... letters can possibly be formed using the above rules such that the third letter of the string is $e?$ $8$ $9$ $10$ $11$
24
Answer the questions on the basis of the information given below. A string of three English letters is formed as per the following rules The first letter is any vowel. The second letter is $m, n$ or $p$. If the second letter is $m,$ then the third letter is any vowel ... is the same as the first letter. How many strings of letters can possibly be formed using the above rules? $40$ $45$ $30$ $35$
25
There are 11 alphabets A, H, I, M, O, T, U, V, W, X, Y, Z. They are called symmetrical alphabets. The remaining alphabets are known as asymmetrical alphabets. How many three-lettered words can be formed such that at least one symmetrical letter is there? $12870$ $18330$ $16420$ None of these
26
A boy is supposed to put a mango into a basket if ordered $1,$ an orange if ordered $2$ and an apple if ordered $3.$ He took out $1$ mango and $1$ orange if ordered $4.$ he was given the following sequence of orders $12332142314223314113234$ At the end of the sequence, what will be the number of fruits in the basket? $10$ $11$ $13$ $17$
27
Answer the following question based on the information given below. Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists of ... the end of the first stage. The number of teams with exactly one win in the second stage of the tournament is $4$
28
Answer the following question based on the information given below. Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists of eight teams, ... to the next stage. What is the number of rounds in the second stage of the tournament? $1$ $2$ $3$ $4$
29
Answer the following question based on the information given below. Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists of eight teams, ... the first stage in spite of which it would be eliminated at the end of first stage? $1$ $2$ $3$ $4$
30
Answer the following question based on the information given below. Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists of eight teams, ... needed for a team in the first stage to guarantee its advancement to the next stage is $5$ $6$ $7$ $4$
31
Answer the following questions based on the information given below. Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists of eight ... advance to the next stage. What is the total number of matches played in the tournament? $28$ $55$ $63$ $35$
32
What is the number of distinct triangles with integral valued sides and perimeter $14?$ $6$ $5$ $4$ $3$
1 vote
33
One red flag, three white flags and two blue flags are arranged in a line such that, no two adjacent flags are of the same colour. the flags at the two ends of the line are of different colours. In how many different ways can the flags be arranged? $6$ $4$ $10$ $2$
34
A boy is supposed to put a mango into a basket if ordered $1,$ an orange if ordered $2$ and an apple if ordered $3.$ He took out $1$ mango and $1$ orange if ordered $4.$ he was given the following sequence of orders $12332142314223314113234$ At the end of the sequence, what will be the number of oranges in the basket? $2$ $3$ $4$ $6$
35
There are 11 alphabets A, H, I, M, O, T, U, V, W, X, Y, Z. They are called symmetrical alphabets. The remaining alphabets are known as asymmetrical alphabets. How many four-lettered passwords can be formed by using symmetrical letters only? (repetitions not allowed) $1086$ $255$ $7920$ None of these
36
In how many ways, we can choose a black and a white square on a chess board such that the two are not in the same row or column? $32$ $96$ $24$ None of these
37
How many numbers between $0$ and one million can be formed using $0, 7$ and $8?$ $486$ $1086$ $728$ None of these
There are $6$ boxes numbered $1, 2, \dots,6.$ Each box is to be filled up with a red or green ball in such a way that at least one box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is $5$ $21$ $33$ $60$
How many three digit positive integers, with digits $x, y$ and $z$ in the hundred's, ten's and unit's place respectively, exist such that $x < y, z < y$ and $x \neq 0?$ $245$ $285$ $240$ $320$
$27$ persons attend a party. Which one of the following statements can never be true? There is a person in the party who is acquainted with all the $26$ members. Each person in the party has a different number of acquaintances. There is a person in the party who has odd number of acquaintances. In the party, there is no set of three mutual acquaintances.