How many words, with or without meaning, can be formed by using the le

1.	How many words, with or without meaning, can be formed by using the letters of the word ‘TRIANGLE’?
Answer» Given, The total number of letters in ‘TRIANGLE’ = 8 To find : number of words, with or without meanings using all the letters of the word like triangel or angletri etc. Formula used : Number of arrangements of n things taken all at a time = P(n, n) P(n, r) = \(\frac{n!}{(n-r)!}\) ∴ The total number of ways in which this can be done = the number of arrangements of 8 things taken all at a time = P(8, 8) = \(\frac{8!}{(8-8)!}\) = \(\frac{8!}{0!}\) {∵ 0! = 1} = 8! Hence, Number of words, with or without meanings using all the letters of the word ‘TRIANGLE’ are 8!.

How many words, with or without meaning, can be formed by using the letters of the word ‘TRIANGLE’?

Answer»

Given,

The total number of letters in ‘TRIANGLE’ = 8

To find : number of words, with or without meanings using all the letters of the word like triangel or angletri etc.

Formula used :

Number of arrangements of n things taken all at a time = P(n, n)

P(n, r) = \(\frac{n!}{(n-r)!}\)

∴ The total number of ways in which this can be done

= the number of arrangements of 8 things taken all at a time

= P(8, 8)

= \(\frac{8!}{(8-8)!}\)

= \(\frac{8!}{0!}\)

{∵ 0! = 1}

= 8!

Hence,

Number of words, with or without meanings using all the letters of the word ‘TRIANGLE’ are 8!.