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Math Help - Sum/Product Rule Question

  1. #1
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    Exclamation 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?
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  2. #2
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    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: . {9\choose5} \:=\:\frac{9!}{5!\,4!} \:=\:126 ways.
    Then the 6 people can be lined up in 6! = 720 ways.

    Answer: . 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: . {8\choose4} \:=\:\frac{8!}{4!\,4!} \:=\:70 ways.
    Then the 6 people can be lined up in 6! = 720 ways.

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

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