How many different words can be formed from the letters of the word ‘GANESHPURI’? In how many of these words:
the letter P and I respectively occupy the first and last place?
Given: the word is ‘GANESHPURI.’
To find: number of words starting with P and ending with I
So, fix the position of first and last letter as P and I
Remaining number of letters in the word = 8
Now, we need to arrange these 8 letters at 8 places.
Formula used:
Number of arrangements of n things taken all at a time = P(n, n)
∴ The total number of ways
= the number of arrangements of 8 things taken all at a time
= P(8, 8)
{∵ 0! = 1}
= 8!
Hence, a possible number of words using letters of ‘GANESHPURI’ starting with ‘P’ and ending with ‘I’ are 8!