# Find the Total Number of Arrangements of the Letters in the Expression A3 B2 C4 When Written at Full Length. - Mathematics

Find the total number of arrangements of the letters in the expression a3 b2 c4 when written at full length.

#### Solution

When expanded, a3 b2 c4   would result in total 9 letters.
This is same as permuting 9 things, of which 3 are similar to the first kind, 2 are similar to the second kind and four are similar to the third kind, i.e. three as , two bs and four cs.
Required number of arrangements =$\frac{9!}{3!2!4!}$= 1260

Concept: Factorial N (N!) Permutations and Combinations
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 16 Permutations
Exercise 16.5 | Q 4 | Page 42