Question

A student is to answer $10$ out of $13$ questions in an examination such that he must choose at least 4 from first five questions. The number of choices available to him is

• A. $196$
• B. $280$
• C. $346$
• D. $140$

Answer 1

Answer: (A)

$196$

The number of choices available to him is

${}^5{C}_9\times {}^8{C}_6+{}^5{C}_5\times {}^8{C}_5$

$=\frac{5!}{4!1!}\times \frac{8!}{6!2!}+\frac{5!}{5!6!}\times \frac{8!}{5!3!}$
$=5\times \frac{8\times 7}{2}+1\times \frac{8\times 7\times 6}{3\times 2}$

$=5\times 4\times 7+8\times 7$

$=140+56$

$=196$