CAT 2019 Set-1 | Question: 63

Question

A supermarket has to place $12$ items (coded A to L) in shelves numbered $1$ to $16$. Five of these items are types of biscuits, three are types of candies and the rest are types of  savouries. Only one item can be kept in a shelf. Items are to be placed such that all items of same type are clustered together with no empty shelf between items of the same type and at least one empty shelf between two different types of items. At most two empty shelves can have consecutive numbers.’

The following additional facts are known.

1. A and B are to be placed in consecutively numbered shelves in increasing order
2. I and J are to be placed in consecutively numbered shelves both higher numbered than the shelves in which A and B are kept.
3. D,E and F are savouries and are to be placed in consecutively numbered shelves in increasing order after all the biscuits and candies.
4. K is to be placed in shelf number $16$.
5. L and J are items of the same type, while H is an item of a different type.
6. C is a candy and is to be placed in a shelf preceded by two empty shelves.
7. L is to be placed in a shelf preceded by exactly one empty shelf.

In how many different ways can the items be arranged on the shelves?

• A. $2$
• B. $8$
• C. $4$
• D. $1$