Pre- cal help with permutations and combinations plz!!?

1) In the game of Yahtzee, five dice are tossed simultaneously. How many outcomes can be distinguished if all the dice are different colors/

2) Mary's lunch always consists of a full plate of salad bar, she always takes equal amounts of each salad she chooses, but she likes to vary her selections. If she can choose from among 9 different salads, how many essentially different lunches can she creates?

3)How many different answer keys are possible for a 10-question True-False test?

4)Six Seniors at Rydell High school meet the qualifications for a competitive honor scholarship at a major university. The university allows the school to nominate up to three candidates, and the school always nominates at least one. How many different choices could the nominating committee make?

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  • 9 years ago
    Favorite Answer

    1) The dice are colored, therefore distinct.

    Each can have any number from 1-6, 6 possibilities,

    5 dice ...6^5 possible outcomes.

    It's more interesting, and difficult, if the dice are not distinct.

    2)

    She can choose anywhere from 1-9 different items, in equal amounts.

    Hence she can choose to include or exclude each of the 9, but not all 9.

    So her number of combinations is 2^9 - 1 (the -1 is to not count the "no items" case)

    Or you can work out: 9c1 + 9c2 + 9c3 + ... + 9c9 but that is a much longer computation.

    3) 2^10

    4) 6c1 + 6c2 + 6c3 = 6 + 15 + 20 ways to nominate either 1, 2, or 3 candidates,

    since it says "up to 3 and at least 1".

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