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Five friends ${F_{1}, F_{2}, F_{3}, F_{4}, F_{5}}_{}$ book five seats ${C_{1}, C_{2}, C_{3}, C_{4}, C_{5}}_{}$ respectively of movie KABIL independently (i.e. $F_{1}$ books $C_{1}$ , $F_{2}$ books $C_{2}$ and so on. In how many different ways they can sit on these seats if $F_{1}$ and $F_{2}$ wants to sit adjacent to each other.

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120

answer is C.

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Detailed Solution

5 friends can be seated in 5! ways.
Choose 2 seats for

F_{1}

and

F_{2}

and this can be done in

C_{2}^{5}

ways.
The other 3 friends can now be seated in 3! ways.
5 friends can sit on these seats if

F_{1}

and

F_{2}

wants to sit adjacent to each other in

C_{2}^{5} \times 3! = 60

ways.

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