Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Prove that 
n C r p r q n – r = npq + n 2 p 2 , if p + q = 1.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
n C r p r q n – r = n . 
. n – 1 C r – 1 p r q n – r
= n. 
= n 
= n[(n – 1)p 2 (p + q) n – 2 + p(p + q) n – 1 ]
= n[np 2 – p 2 + p] = n 2 p 2 – np 2 + pn = n 2 p 2 + npq
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
The co-efficient of y in the expansion of (y 2 +c/y) 5 is
The sum of coefficients in (x + 2y + z) 10 =
Given positive integers, r > 1, n > 2 and the coefficients of (3r) th and (r + 2) th terms in the b…
The sum of the coefficients in the expension of (1 + 2x + 3x 2 +……..nx n ) 2 is -
The sum of the coefficient in the expansion of (1 + 5x – 7x 3 ) 3165 is -
If the coefficients of second, third and fourth term in the expansion of are in A.P., then is equ…