We know that ^nC_r=n!/r!(n r)!Given, ^14C_3Where n=14, r=3∴^14C_3=14!/3!(14 3)!0ex0ex =14!/3!11!0ex0ex =14× 13× 12× 11!/3× 2× 1× 11!0ex0ex ...

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Product Rule of Differentiation

Evaluate: 14C...

Question

Evaluate: $^{14} C_{3} .$

$42$

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$364$

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$146$

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$328$

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Solution

The correct option is B
$364$

We know that
$^{n} C_{r} = \frac{n!}{r! (n - r)!}$
Given, $^{14} C_{3}$
Where $n = 14, r = 3$
$∴^{14} C_{3} = \frac{14!}{3! (14 - 3)!} = \frac{14!}{3! 11!} = \frac{14 \times 13 \times 12 \times 11!}{3 \times 2 \times 1 \times 11!} = \frac{14 \times 13 \times 12}{3 \times 2 \times 1} = \frac{2184}{6} = 364$
Thus, $^{14} C_{3}$ $= 364$
Hence, option (B) is the correct option.

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14 - [21 - {28 - (14 - 1)}]

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