Question

Ten members of a wedding party are lining up in a row for a photograph. How many ways are there to line up the ten people? How many ways are there to line up the ten people if the groom must be to the immediate left of the bride in the photo? How many ways are there to line up the ten people if the groom must be next to the bride (either on her left to right side)?

Answer 1

a) 10!

b) 9!

c) 2*9!

Explanation:

a) Total number of ways in which ten people can be lined up is

`10!`

b) Total number of ways in which ten people can be lined up if the groom must be to the immediate left of the bride in the photo

- Suppose if the bride stands at the 10th position , there will be only one way in which the groom can be at the immediate left side of the bride

Like wise for all positions i.e 9th, 8th , 7th , 6th, 5th, 4th, 3rd, 2nd , there will be only one way in which the groom can be at the immediate left side of the bride

So in totality there are 9 ways.

c) In the way as done in part (b) , the number of ways to line up the ten people if the groom must be next to the bride (either on left or right)

`= 2*9!`

Answer 2

(a) 10!

(b) 9!

(c) 2!9!

Explanation:

(a)

Total number of members = 10

We need to line up the ten people.

Total number of ways to arrange n terms is n!. Similarly, total number of ways to line up the ten people is

`\text{Total ways} =10!`

Therefore the total number of ways to line up the ten people is 10!.

(b)

Let groom is immediate left of the bride it means both will sit together. So we need to arrange peoples for total 9 places (8 of others and 1 of bride and groom).

`\text{Total ways} =9!1!1!=9!`

Therefore the number of ways to line up the ten people if the groom must be to the immediate left of the bride in the photo is 9!.

(c)

Let groom is immediate left of the bride it means both will sit together. So we need to arrange peoples for total 9 places (8 of others and 1 of bride and groom).

Bride and groom can interchange there sits.

Total number of ways to arrange bride and groom = 2!

`\text{Total ways} =9!2!`

Therefore the number of ways to line up the ten people if the groom must be next to the bride (either on her left to right side) is 9!2!.