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 three of the first five questions, is

• Correct answer
  A

  $276$
• B

  $600$
• C

  $840$
• D

  $640$

Solution

The possible cases are:
Required number of ways $={{}_{}{}^{5}C}_3\times {{}_{}{}^{8}C}_7+{{}_{}{}^{5}C}_4\times {{}_{}{}^{8}C}_6+{{}_{}{}^{5}C}_5\times {{}_{}{}^{8}C}_5$
$=\frac{5\times 4}{2}\times 8+5\times \frac{8\times 7}{2}+\frac{1\times 8\times 7\times 6}{3\times 2}$
$=80+140+56=276$

Hence, the correct answer is option: 'A'.