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anonymous

  • one year ago

For The Questions, a club has 10 members. a. Find the number of different slates of 3 officers (list of president, vice-president, and treasurer) that the club could have for officers. b.Find the number of different slates of 4 officers (list of president, vice-president, secretary, and treasurer) that the club could have for officers.

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  1. anonymous
    • one year ago
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    Are you studying combinations and permutations?

  2. anonymous
    • one year ago
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    Yes

  3. anonymous
    • one year ago
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    Is this question a combination or a permutation? What do you think?

  4. anonymous
    • one year ago
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    Remember that order doesn't matter in a combination but order does matter in a permutation.

  5. anonymous
    • one year ago
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    i think the first one is a permutation

  6. anonymous
    • one year ago
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    Right you are. In fact, they both are. Can you see that?

  7. anonymous
    • one year ago
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    Yes, because they have to be in a certain order, right?

  8. anonymous
    • one year ago
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    So, in the first question, you need to calculate\[_3 P_{10}\]Can you do that?

  9. anonymous
    • one year ago
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    I'm not sure how too

  10. anonymous
    • one year ago
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    Actually, my notation was backwards. Sorry. The general equation for permutations is\[_{n}P_r=\frac{ n! }{\left( n-r \right) !}\]And in the first question n=10 and r=3. Can you take it from here?

  11. anonymous
    • one year ago
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    I got -2 that's probably not correct is it?

  12. anonymous
    • one year ago
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    Not quite. The equation becomes\[_{10}P_3=\frac{ 10! }{ 7! }\]If you write out the factorial multiplications you'll see that all the factors from 7 down will cancel.

  13. anonymous
    • one year ago
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    Something like\[_{10}P_3=\frac{ 10\times9\times8\times7\times6\times5\times4\times3\times2\times1 }{ 7\times6\times5\times4\times3\times2\times1}\]

  14. anonymous
    • one year ago
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    See. Everything from 7 down will cancel out leaving\[_{10}P_3=10\times9\times8=?\]

  15. anonymous
    • one year ago
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    720? that's what I got from the multiplication

  16. anonymous
    • one year ago
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    Excellent. Now try the second question by yourself. You need to calculate\[_{10}P_4\]

  17. anonymous
    • one year ago
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    5040?

  18. anonymous
    • one year ago
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    Terrific. Well done.

  19. anonymous
    • one year ago
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    Thanks!

  20. anonymous
    • one year ago
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    You're welcome

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