Find the number of ways of selecting 8 subjects from 12 subjects for an examination
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Correct Answer: Option B
Explanation:
Combination is the number (n) of ways of selecting a number of (m) of objects from n
\(^{12}C_{8}\frac{12!}{8!(12-8)!}\\=\frac{12!}{8!4!}\\\frac{(12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1)}{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}\\After\hspace{1mm} cancelling \hspace{1mm}out \hspace{1mm}we\hspace{1mm} have\\11\times 5\times 9 = 495 \)
Combination is the number (n) of ways of selecting a number of (m) of objects from n
\(^{12}C_{8}\frac{12!}{8!(12-8)!}\\=\frac{12!}{8!4!}\\\frac{(12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1)}{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}\\After\hspace{1mm} cancelling \hspace{1mm}out \hspace{1mm}we\hspace{1mm} have\\11\times 5\times 9 = 495 \)