Question

How many different 10-letter words (real or imaginary) can be formed from the letters of the word LITERATURE?

Answer 1

The number of words that can be formed from the word "LITERATURE" is 453600

Explanation:

Given

Word: LITERATURE

Required: Number of 10 letter word that can be formed

The number of letters in the word "LITERATURE" is 10

But some letters are repeated; These letters are T, E and R.

Each of the letters are repeated twice (2 times)

i.e.

Number of T = 2

Number of E = 2

Number of R = 2

To calculate the number of words that can be formed, the total number of possible arrangements will be divided by arrangement of each repeated character. This is done as follows;

Number of words that can be formed =
`(10!)/(2!2!2!)`

Number of words =
`(10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)/(2 * 1 * 2 * 1 * 2 * 1)`

Number of words =
`(3628800)/(8)`

Number of words = 453600

Hence, the number of words that can be formed from the word "LITERATURE" is 453600