Question

A student has to answer $10$ out $13$ question in an examination. The number of ways in which he can answer if he must answer atleast $3$ of the first five question is :

• A. $276$
• B. $267$
• C. $80$
• D. $1200$

Answer 1

The correct option is A $276$

If the student answers $3$ questions from the first five questions then he can choose $7$ questions from the remaining $8$ questions. Therefore number of combinations will be

${=}^5{C}_3{\times }^8{C}_7$

$=10\times 8$

$=80$

If the student answers $4$ questions from the first five questions he can choose $6$ questions from the remaining $8$ questions. Which will be

${=}^5{C}_4{\times }^8{C}_6$

$=5\times 28$

$=140$

If the student answers $5$ questions from the first five questions he can choose $5$ questions from the remaining $8$ questions. Which will be

${=}^5{C}_5{\times }^8{C}_5$

$=1\times 56$

$=56$

Therefore, the total number of choices $=80+140+56=276$

Hence, this is the answer.