The letter G always occupies the first place?

Question

How many different words can be formed from the letters of the word ‘GANESHPURI’? In how many of these words : 

The letter G always occupies the first place?

Answer 1

Given : the word is ‘GANESHPURI.’ 

To find : number of words starting with G So, fix the position of the first letter as G

So, fix the position of the first letter as G.

G

 

Remaining number of letters in the word = 9  

Now, 

We need to arrange these 9 letters at 9 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 9 things taken all at a time 

= P(9, 9)

= \(\frac{9!}{(9-9)!}\)

= \(\frac{9!}{0!}\)

{∵ 0! = 1} = 9! 

Hence, 

A possible number of words using letters of ‘GANESHPURI’ starting with ‘G’ is 9!