Question #acec1

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Question #acec1

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Answer 1 · 2016-11-27T22:17:34

Formula for combinations:
$C (n, r) = \frac{n!}{r! (n - r)!}$ $C(n,r)=frac{n!}{r!(n-r)!}$

Let $n = 10$ $n=10$ , and let $r = 6$ $r=6$

$C (10, 6) = \frac{10!}{6! (10 - 6)!}$ $C(10,6)=frac{10!}{6!(10-6)!}$

$= \frac{10!}{6! \cdot 4!}$ $=frac{10!}{6!*4!}$

$= \frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$ $=frac{10*9*8*7*6*5*4*3*2*1}{6*5*4*3*2*1*4*3*2*1}$

$=frac{10*color(blue)(9)*color(green)(8)*7*cancel(6*5)*cancel(4*3*2*1)}{cancel(6*5)*color(green)(4)*color(blue)(3)*color(green)(2)*1*cancel(4*3*2*1)}$

$=frac{10*3*7}{1}$

$=210$

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Question #acec1

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