# Find the Number of Words Formed by Permuting All the Letters of the Following Words:Intermediate - Mathematics

Find the number of words formed by permuting all the letters of the following words:
INTERMEDIATE

#### Solution

This word consists of 12 letters that include two Is, two Ts and three Es.
The total number of words is the number of arrangements of 12 things, of which 2 are similar to one kind, 2 are similar to the second kind and 3 are similar to the third kind.
⇒$\frac{12!}{2!2!3!}$= 19958400

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 1.2 | Page 42