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Question
5C1 + 5C2 + 5C3 + 5C4 +5C5 is equal to
Options
30
31
32
33
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Solution
31
\[= 2 \times^5 C_1 + 2 \times {}^5 C_2 +^5 C_5 \]
\[ = 2 \times 5 + 2 \times \frac{5!}{2! 3!} + 1 \]
\[ = 10 + 20 + 1 \]
\[ = 31\]
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