Question

Find the total number of arrangements of the letters in the expression $a^3{b}^2{c}^4$ when written at full length.

Answer 1

There are 3a' s, 2b's and 4c' s.
So, the number of arrangements=$\frac{9!}{4!3!2!}$
=$\frac{9\times 8\times 7\times 6\times 5\times 4}{4!\times 3\times 2\times 2}$
= $9\times 4\times 7\times 5$ = 1260.
Hence, the total number of arrangements are 1260.