BITSAT2017MathematicsPermutation and CombinationActual
The value of ∑ r = 1 10 r · C r n C r - 1 n is equal to
Options
- A5 2 n - 9
- B10 n
- C9 ( n - 4 )
- DNone of these
Correct answer
A. 5 2 n - 9
Step-by-step solution
We have, ∑ r = 1 10 r · C r n C r - 1 n = ∑ r = 1 10 n - r + 1 ⇒   ∑ r = 1 10 r · C r n C r - 1 n = ∑ r = 1 10 n + 1 - r ⇒   ∑ r = 1 10 r · C r n C r - 1 n = 10 n + 1 - ∑ r = 1 10 r ⇒   ∑ r = 1 10 r · C r n C r - 1 n = 10 n + 1 - 55 = 10 n - 45 = 5 2 n - 9