Question

A student have to answer $10$ out of $13$ questions in an examination. The number of ways in which he can answer if he must answer at least $3$ of the first five questions is

Answer 1

Number of ways.

${}^5{C}_3{\times }^8{C}_7{+}^5{C}_4{\times }^8{C}_6{+}^5{C}_5{\times }^8{C}_5$

$=(10\times 8)+(5\times 28)+(1\times 56)$

$=80+140+56$

$=276$