NTA Abhyas JEE Main2020MathematicsPermutation and CombinationPractice
The number of ways in which 2 n distinct letters (addressed) can be distributed in N distinct mail boxes such that there are exactly K letters n < K ≤ 2 n in one of the mail boxes is
Options
- AC 2 n K ⋅ N
- BC K 2 n · N N - 1 2 n - K
- CC 2 n K N - 1 2 n - K
- DC 2 n K 2 n - K N - 1 ⋅ N
Correct answer
B. C K 2 n · N N - 1 2 n - K
Step-by-step solution
Select K letters from 2 n in C 2 n K ways. Select 1 of the mail boxes in C N 1 way. Remaining 2 n - K letters each have N - 1 options and can be allotted in N - 1 2 n - K ways. Hence, the required number of ways = C K 2 n C 1 N N - 1 2 n - K .