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A student has to answer 10 out of 13 questions in an examination. The number of ways in which he can answer if he must answer atleast 3 of the first five questions is
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1165 Upvotes
Verified Answer
The correct answer is:
276
Total number of ways
$$
\begin{aligned}
& ={ }^5 C_3{ }^8 C_7+{ }^5 C_4{ }^8 C_6+{ }^5 C_5{ }^8 C_5 \\
& =10 \times 8+5 \times 28+1 \times 56 \\
& =80+140+56=276
\end{aligned}
$$
$$
\begin{aligned}
& ={ }^5 C_3{ }^8 C_7+{ }^5 C_4{ }^8 C_6+{ }^5 C_5{ }^8 C_5 \\
& =10 \times 8+5 \times 28+1 \times 56 \\
& =80+140+56=276
\end{aligned}
$$
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