retagged by
463 views

1 Answer

1 votes
1 votes

A man can invite exactly $3$ girls from $5$ girls $=\;^{5}C_{3} = \frac{5!}{2!3!}  = \frac{5 \times 4 \times 3!}{2 \times 1 \times 3!}=10$ ways

Now, boys can be invited $0,1,2,3, \text{(or)}\;4$

Number of ways boys can be invited $ = \;^{4}C_{0} + \;^{4}C_{1} + \;^{4}C_{2} + \;^{4}C_{3} + \;^{4}C_{4} = 1 + 4 + 6 + 4 +1 = 16$ ways

$\therefore$ The total number of ways $ = 10 \times 16 = 160$ ways.

Correct Answer $:160$

$\textbf{PS:}$

  • $\;^{n}C_{0} + \;^{n}C_{1} + \;^{n}C_{2} + \dots + \;^{n}C_{n} = 2^{n}$
  • The number of ways to pick $‘r\text{’}$ unordered element from an $‘n\text{’}$ element set is $\;^{n}C_{r} = \frac{n!}{(n-r)!r!}$
edited by
Answer:

Related questions

2 votes
2 votes
1 answer
2
go_editor asked Mar 19, 2020
695 views
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 a...
0 votes
0 votes
0 answers
3
go_editor asked Mar 11, 2020
497 views
A cube of side $12\; \text{cm}$ is painted red on all the faces and then cut into smaller cubes, each of side $3 \text{cm}$. What is the total number of smaller cubes hav...
0 votes
0 votes
0 answers
5