1. ## Sum/Product Rule Question

If you could help solve this just using addition and multiplication (sum and product rule) it would be greatly appreciated!!! Thank you in advance!

Question: In how many ways can a photographer at a wedding arrange 6 people in a row from a group of 10 which include the bride and groom if...

A.) the bride must be in the picture?

B.)
both the bride and the groom must be in the picture?

2. Hello, fusion1455!

In how many ways can a photographer at a wedding arrange 6 people in a row
from a group of 10 which include the bride and groom if:

A) the bride must be in the picture?
The bride is in the picture.
Then we choose 5 more people from the remaining 9 people.
. . There are: .$\displaystyle {9\choose5} \:=\:\frac{9!}{5!\,4!} \:=\:126$ ways.
Then the 6 people can be lined up in $\displaystyle 6! = 720$ ways.

Answer: .$\displaystyle 126 \times 720 \:=\:90,\!720$

B) both the bride and the groom must be in the picture?
The bride and groom are in the picture.
Then we choose 4 more people from the remaining 8 people.
. . There are: .$\displaystyle {8\choose4} \:=\:\frac{8!}{4!\,4!} \:=\:70$ ways.
Then the 6 people can be lined up in $\displaystyle 6! = 720$ ways.

Answer: .$\displaystyle 70 \times 720 \:=\:50,\!400$