First slide

Binomial theorem for positive integral Index

Question

The number of terms in the expansion of the multinomial ${(x + y + z)}^{n}$

Moderate

A

$\frac{1}{2} (n + 1) (n + 2)$
B

$\frac{1}{2} n (n + 1)$
C

$\frac{1}{2} (n + 1) (n + 3)$
D

none of these

Solution

Number of terms in ${(x + y + z)}^{n}$
= number of non-negative integral solution of $p + q + r = n$
$=^{n + 2} C_{2} = \frac{1}{2} (n + 2) (n + 1)$

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