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anonymous

  • 5 years ago

A small start-up company with 16 employees will select its 4 board members from among the employees. How many different groups of board members are possible?

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  1. anonymous
    • 5 years ago
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    now this is just the same as the previous one. you need \[\dbinom{16}{4}\] do you know how to compute \[\dbinom{n}{k}\] ?

  2. anonymous
    • 5 years ago
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    i dont think the last one was right lol it was actually some really large number

  3. anonymous
    • 5 years ago
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    well then it was because 'itinerary' meant the order mattered. so it was \[10\times 9\times 8\times7=5040\]

  4. anonymous
    • 5 years ago
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    yes! so then i do 16*15*14*13?

  5. anonymous
    • 5 years ago
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    but in this problem order does not matter, just who is selected. so this time it really is \[\dbinom{16}{4}\]

  6. anonymous
    • 5 years ago
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    Yes, you start out with 16*15*14*13 but this case is different because in this case you do not care in which order the people were picked. so you have do divide by the number of ways you can permute the 4 people, which is 4*3*2

  7. anonymous
    • 5 years ago
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    divide first, multiply last. \[\dbinom{16}{4}=\frac{16 \times 15\times 14\times 13}{4 \times 3\times2}\]

  8. anonymous
    • 5 years ago
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    1820?

  9. anonymous
    • 5 years ago
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    \[=8\times 5\times 14\times 13\]

  10. anonymous
    • 5 years ago
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    oops sorry

  11. anonymous
    • 5 years ago
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    2*5*14*13=1820

  12. anonymous
    • 5 years ago
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    you are right. i canceled incorrectly. sorry.

  13. anonymous
    • 5 years ago
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    no worries i just multiplied and then divided im lucky ahah

  14. anonymous
    • 5 years ago
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    that always works with a calculator. but the answer is always a whole number (because the question is "how many") so you can always cancel the entire denominator.

  15. anonymous
    • 5 years ago
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    Oh I see, thank you very mch!

  16. anonymous
    • 5 years ago
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    welcome.

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