How many `5`-letter words, with or without meaning, can be formed out of the letters of the word `EQUATIONS` if repetition of letters is not allowed ?

Options

A. `126`
B. `5^(9)`
C. `9^(5)`
D. `15120`

Answer

D

Explanation

There are 9 letters in the word, 'EQUATIONS'. In order to construct 5-letter words from these 9 letters, we first select 5 letter out of these 9 letters and then the selected letters are arranged. So, the job of construction of 5 letter words is divided into two sub-jobs.
`J_(1)` : Selecting 5 letters from 9 letters of the word ''EQUATIONS'' .
`J_(2)` : Arranging 5 selected from 9 letters to form 5 letter words is . We find that job `J_(1)` can be completed in `^(9)C_(5)` ways and job `J_(2)` in 5! ways.
`:.` Total number of 5 letter words `=^(9)C_(5)xx5!""=15120`