How do you evaluate 6C3?

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How do you evaluate 6C3?

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Answer 1 · 2016-07-21T12:44:48

$^{6} C_{3} = 20$ $""^6C_3=20$

Explanation:

$^{n} C_{r}$ $""^nC_r$ is selection of $r$ $r$ possible combinations of objects from a set of $n$ $n$ objects.

Mathematically $^{n} C_{r} = \frac{n!}{r! \times (n - r)!}$ $""^nC_r=(n!)/(r!xx(n-r)!)$

Hence $^{6} C_{3} = \frac{6!}{3! \times (6 - 3)!}$ $""^6C_3=(6!)/(3!xx(6-3)!)$

= $\frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{(3 \times 2 \times 1) \times (3 \times 2 \times 1)}$ $(6xx5xx4xx3xx2xx1)/((3xx2xx1)xx(3xx2xx1))$

= $\frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 5 \times 4 = 20$ $(6xx5xx4)/(3xx2xx1)=5xx4=20$

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How do you evaluate 6C3?

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