Question
Question: <sup>n</sup>C<sub>r–1</sub> + 3 <sup>n</sup>C<sub>r</sub> + 3 <sup>n</sup>C<sub>r+1</sub> + <sup>n</...
nCr–1 + 3 nCr + 3 nCr+1 + nCr+2 is equal to
A
n+2Cr+1
B
n+2Cr+2
C
n+2Cr+3
D
n+3Cr+2
Answer
n+3Cr+2
Explanation
Solution
nCr–1 + nCr + 2(nCr + nCr+1) + nCr+1 + nCr+2
= n+1Cr + 2 n+1Cr+1 + n+1Cr+2
= n+1Cr + n+1Cr+1 + n+1Cr+1 + n+1Cr+2
= n+2Cr+1 + n+2Cr+2 = n+3Cr+2