# Sum/Product Rule Question

• Apr 7th 2009, 06:03 PM
fusion1455
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?
• Apr 7th 2009, 07:16 PM
Soroban
Hello, fusion1455!

Quote:

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

Quote:

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