exam Maths Puzzle

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

A.

29P7

B.

29C7

C.

28P7

D.

29C7

Read Solution (Total 3)

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. 29P7 ways.
11 years agoHelpfull: Yes(2) No(1)

blank chairs 28
interspace among them 29
29p7
10 years agoHelpfull: Yes(1) No(2)
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. 29P7 ways.
7 years agoHelpfull: Yes(0) No(0)

exam Other Question

There are eight boxes of chocolates, each box containing distinct number of chocolates from 1 to 8. In how many ways four of these boxes can be given to four persons (one boxes to each) such that the first person gets more chocolates than each of the three, the second person gets more chocolates than the third as well as the fourth persons and the third person gets more chocolates than fourth person?

A.

35

B.

70

C.

105

D.

210

There are 2 brothers among a group of 20 persons. In how many ways can the group be arranged around a circle so that there is exactly one person between the two brothers?

A.

2 × 17!

B.

18! × 18

C.

19! × 18

D.

2 × 18!

E.

2 × 17! × 17!