Question

A question paper consisting of 10 questions is divided into 3 parts with 5, 3, 2 questions. A candidate is to answer 6 questions without neglecting any part. The number of ways in which he can make up his choice is:

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

Answer 1

Answer: (A)

$175$

Selection pattern is,

Part 1 (5)	Part 2 (3)	Part 3 (2)
1	3	2
3	1	2
3	2	1
2	3	1
2	2	2
4	1	1

Hence required number of ways ${=}^5{C}_1{.}^3{C}_3{.}^2{C}_2{+}^5{C}_3{.}^3{C}_1{.}^2{C}_2{+}^5{C}_3{.}^3{C}_2{.}^2{C}_1{+}^5{C}_2{.}^3{C}_3{.}^2{C}_1{+}^5{C}_2{.}^3{C}_2{.}^2{C}_2{+}^5{C}_4{.}^3{C}_1{.}^2{C}_1=175$