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Find the number of ways of selecting 8 subjects from 12 s...

Find the number of ways of selecting 8 subjects from 12 subjects for an examination

A.

490

B.

495

C.

496

D.

498

View answer & explanation

Correct answer is B

Combination is the number (n) of ways of selecting a number of (m) of objects from n
$^{12}C_{8}\frac{12!}{8!(12-8)!}\\=\frac{12!}{8!4!}\\\frac{(12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1)}{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}\\After\hspace{1mm} cancelling \hspace{1mm}out \hspace{1mm}we\hspace{1mm} have\\11\times 5\times 9 = 495$

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