Question

The number of terms in the expansion of $(a+b+c+d{)}^{15}$ is , if $a\ne b\ne c\ne d$

• A. $220$
• B. $816$
• C. $495$
• D. None of the above

Answer 1

Answer: (B)

$816$

For $(a+b+c....+t{)}^n$,
the total number of terms will be
$\frac{(n+1)(n+2)(n+3)...(n+t-1)}{(t-1)!}$
In this case, $t=4$, $n=15$. Hence, the total number of terms
$=\frac{\mathrm{16.17.18}}{6}$
$=\mathrm{16.17.3}$
$=816$