anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
now this is just the same as the previous one. you need \[\dbinom{16}{4}\] do you know how to compute \[\dbinom{n}{k}\] ?
anonymous
  • anonymous
i dont think the last one was right lol it was actually some really large number
anonymous
  • anonymous
well then it was because 'itinerary' meant the order mattered. so it was \[10\times 9\times 8\times7=5040\]

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anonymous
  • anonymous
yes! so then i do 16*15*14*13?
anonymous
  • anonymous
but in this problem order does not matter, just who is selected. so this time it really is \[\dbinom{16}{4}\]
anonymous
  • anonymous
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
anonymous
  • anonymous
divide first, multiply last. \[\dbinom{16}{4}=\frac{16 \times 15\times 14\times 13}{4 \times 3\times2}\]
anonymous
  • anonymous
1820?
anonymous
  • anonymous
\[=8\times 5\times 14\times 13\]
anonymous
  • anonymous
oops sorry
anonymous
  • anonymous
2*5*14*13=1820
anonymous
  • anonymous
you are right. i canceled incorrectly. sorry.
anonymous
  • anonymous
no worries i just multiplied and then divided im lucky ahah
anonymous
  • anonymous
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.
anonymous
  • anonymous
Oh I see, thank you very mch!
anonymous
  • anonymous
welcome.

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