Question

In how many ways can a photographer at a wedding arrange 5 people in a row, including the bride and groom, if

(a) the bride must next to the groom?

(b) the bride is not next to the groom?

(c) the bride is positioned somewhere to the left of the groom?

Answer 1

a) Given that the bride must be next to the groom, number of ways that the 5 people could be arranged here is computed as:

= (Number of ways to arrange 3 people and the bride groom group ) * Number of permutations of bride groom

= 4! * 2!

= 48

Therefore there are 48 ways to arrange the people here.

b) Number of ways to arrange the 5 people such that bride is not next to the groom is computed here as:

= Total number of ways to arrange the 5 people - Number of ways to arrange 5 people such that both bride and groom are together

= 5! - 48

= 72

Therefore there are 72 ways to arrange the people here.

c) There are 2 ways for the bride to be placed either left or right with equal probability. Therefore the number of ways that 5 people could be positioned such that bride is positioned somewhere to the left of the groom is computed here as:

= 5! / 2

= 60

Therefore there are 60 ways to arrange the 5 people here.