Permutation-Combination
Aptitude

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Q.

In how many ways can seven friends be seated in a row having 35 seats, such that no two friends occupy adjacent seats?

 A.

${^{29}P_7}$

 B.

${^{29}C_7}$

 C.

${^{28}P_7}$

 D.

${^{29}C_7}$

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Solution:
Option(A) is correct

First let us consider the 28 unoccupied seats.

They create 29 slots- one on the left of each seat and one on the right of the last one.

We can place the 7 friends in any of these 29 slots i.e. ${^{29}P_7}$ ways.


(1) Comment(s)


Snehal
 ()

I believe the better explanation is there should be a gap between each friend......

which means a min of 6 empty seats between them if they are sitting closest to each other....like X_X_X_X (X=occupied seat, _ = empty seat )......

This leaves 29 available seats. 7 friends can occupy them 29P7 ways