We know that ^nC_r=n!/r!(n r)!Given ^6C_3Where n=6, r=3∴^nC_r=n!/r!(n r)!0ex0ex =6!/3!(6 3)!0ex0ex =6!/3!(3)!0ex0ex =6× 5× 4× 3!/3!× 3× ...

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Product Rule of Differentiation

Evaluate 6C3

Question

Evaluate $^{6} C_{3}$

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Solution

We know that
$^{n} C_{r} = \frac{n!}{r! (n - r)!}$
Given $^{6} C_{3}$
Where $n = 6, r = 3$
$∴^{n} C_{r} = \frac{n!}{r! (n - r)!} = \frac{6!}{3! (6 - 3)!} = \frac{6!}{3! (3)!} = \frac{6 \times 5 \times 4 \times 3!}{3! \times 3 \times 2 \times 1} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = \frac{120}{6} = 20$
Hence, $^{6} C_{3}$ is $20$

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