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!.