First slide

Multinomial expansion

Question

The number of terms in the expansion of ${(x_{1} + x_{2} + . . . . . . + x_{r})}^{n}$ is

Moderate

A

$^{n + 1} C_{r}$
B

$n + r - 1_{C_{r - 1}}$
C

$n + r + 1_{C_{r + 1}}$
D

$^{n + r - 1} C_{r}$

Solution

${(x_{1} + x_{2} + . . . . . . + x_{r})}^{n} n o o f t e r m s = {n + r - 1}_{C_{r - 1}}$

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