Question

Ten members of a wedding party are lining up in a row for a photograph.

a. How many ways are there to line up the 10 people?
b. How many ways are there to line up the 10 people if the groom must be to the immediate left of the bride in the photo?
c. How many ways are there to line up the 10 people if the groom must be next to the bride (on either her left of right side)?

Answer 1

Part (A): 10!=3,628,800

Part (B): 9! = 362880

Part (C): 9!2! = 725,760

Explanation:

Consider the provided information.

Part (A) How many ways are there to line up the 10 people?

Total number of members = 10

Number of ways to arrange n terms is n!.

Therefore, the number of ways to arrange 10 people is 10!

`\text{Total ways} =10!=3628800`

Part (b) How many ways are there to line up the 10 people if the groom must be to the immediate left of the bride in the photo?

If groom is immediate left of the bride that means we only need to arrange peoples for total 9 places (8 of others and 1 of bride and groom).

Therefore, the number of ways are = 9! = 362880

Part (c) How many ways are there to line up the 10 people if the groom must be next to the bride (on either her left of right side)?

Groom must be next to the bride means either her left of right side.

Therefore, total number of ways to arrange bride and groom = 2!

Take bride and groom as 1 person.

So we need to arrange peoples for total 9 places (8 of others and 1 of bride and groom).

Therefore, the total number of ways are = 9!2! = 725,760