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Math

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I fell asleep trying to figure this one out ... if you could help I would appreciate it ... Here is the problem ..
If Jon, Mac, and Heather are taking a group photo, how many different ways can the photographer line them up? .. okay, I have that one .. = 6 ... but now i have to add 3 more people and try to figure out how many ways can all of these together (6 of them)be lined up .... is there a formula i a could I use instead of writing all the different combinations? .. thank you for your help!

  • Math -

    Wouldn't it be six factorial?

  • Math -

    Yes, i understand that but can't figure out with what or how many different ways ..

  • Math -

    Think of it as filling three spots with the three different people.

    You can place one of 3 different people in the first spot.
    Now look at the second spot, since one of the people has been placed, that would leave one of the remaining two people to be placed in that spot

    So far you have 3*2 ways.

    Finally since there is only one person left to placed in the last spot,
    your calculations is 3*2*1 or 6 ways.

  • Math -

    continued....

    so if you had 6 people, repeat the thinking process and you have, as bobpursely told you,
    6*5*4*3*2*1 = 6! = 720

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