Question

The total number of arrangements of letter $a^5{b}^4{c}^6$ when written at full length is

• A. $\frac{15!}{3!\cdot 4!\cdot 5!}$
• B. $\frac{15!}{6!\cdot 5!\cdot 7!}$
• C. $\frac{15!}{5!\cdot 4!\cdot 6!}$
• D. $\frac{15!}{4!\cdot 5!}$

Answer 1

The correct option is C $\frac{15!}{5!\cdot 4!\cdot 6!}$

Given letter : $a^5{b}^4{c}^6$,
when written at full length $\Rightarrow aaaaabbbbcccccc$
Total letters $=15(5a^{\prime }s+4b^{\prime }s+6c^{\prime }s)$
$\therefore$ The total arrangements
$=\frac{15!}{5!\cdot 4!\cdot 6!}$