What's 10P5? What's 9C3?

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Answer 1 · 2017-02-26T12:11:43

$P_{10, 5} = 30, 240; C_{9, 3} = 84$ $P_(10,5)=30,240; C_(9,3)=84$

$P_{10, 5}$ $P_(10,5)$

This is the permutation of a population of 10, choosing 5. The general formula for a permutation is:

$P_{n, k} = \frac{n!}{(n - k)!}; n = population, k = picks$ $P_(n,k)=(n!)/((n-k)!); n="population", k="picks"$

$P_{10, 5} = \frac{10!}{(10 - 5)!} = \frac{10!}{5!} \Rightarrow$ $P_(10,5)=(10!)/((10-5)!)=(10!)/(5!)=>$

$10 \times 9 \times 8 \times 7 \times 6 = 30, 240$ $10xx9xx8xx7xx6=30,240$

$C_{9, 3}$ $C_(9,3)$

This is the combination of a population of 9, choosing 3. The general formula for a combination is:

$C_{n, k} = \frac{n!}{(k)! (n - k)!}$ $C_(n,k)=(n!)/((k)!(n-k)!)$ with $n = population, k = picks$ $n="population", k="picks"$

$C_{9, 3} = \frac{9!}{(3)! (9 - 3)!} = \frac{9!}{(3!) (6!)} \Rightarrow$ $C_(9,3)=(9!)/((3)!(9-3)!)=(9!)/((3!)(6!))=>$

$(cancel9^3xxcancel8^4xx7xxcancel(6!))/(cancel3xxcancel2xxcancel(6!))=3xx4xx7=84$