# Moderate Permutation-Combination Solved QuestionAptitude Discussion

 Q. A student is required to answer 6 out of 10 questions divided into two groups each containing 5 questions. He is not permitted to attempt more than 4 from each group. In how many ways can he make the choice?
 ✖ A. 210 ✖ B. 150 ✖ C. 100 ✔ D. 200

Solution:
Option(D) is correct

Number of ways of choosing 6 from 10,

$= {^{10}C_6}$

$=210$

Number of ways of attempting more than 4 from a group:

$=2×{^5C_5}×{^5C_1}$

$= 10$

⇒ Required number of ways,

$= 210 - 10$

$= \textbf{200}$