Question

A question paper consisting of $10$ questions which is divided into $3$ parts with $5,3,2$ questions respectively. A candidate is to answer $6$ questions without neglecting a question from any part. The number of ways in which he can answer the paper is

• A. $175$
• B. $200$
• C. $225$
• D. $150$

Answer 1

The correct option is A $175$

Number of ways in which candidate can answer without neglecting a quesion from any part
$={}^5{C}_4\cdot {}^3{C}_1\cdot {}^2{C}_1+{}^5{C}_3\cdot {}^3{C}_2\cdot {}^2{C}_1+{}^5{C}_3\cdot {}^3{C}_1\cdot {}^2{C}_2+{}^5{C}_2\cdot {}^3{C}_3\cdot {}^2{C}_1+{}^5{C}_2\cdot {}^3{C}_2\cdot {}^2{C}_2+{}^5{C}_1\cdot {}^3{C}_3\cdot {}^2{C}_2=30+60+30+20+30+5=175$