The letter P and I respectively occupy the first and last place?

Question

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?

Answer 1

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)

P(n, r) = \(\frac{n!}{(n-r)!}\)

∴ The total number of ways = 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,

A possible number of words using letters of ‘GANESHPURI’ starting with ‘P’ and ending with ‘I’ are 8!