Aptitude Discussion

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. |
${^{29}C_7}$ |

**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.

**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