Question

How many distinct 9-letter words starting with “i” can be formed from the word “committee”?

Answer 1

5040

Explanation:

Step 1:

Distinct 9-letter words formed from the word "COMMITTEE" is equal to the number of different permutations for word "COMMITTEE".

Step 2:

Now, if in the 9-letter word the first letter is fixed as "i". Then number of distinct words formed will be equal to number of different permutation for the word "COMMTTEE".

Step 3:

Now, the as it is known that number of permutation of n distinct object where p, q and r distinct object are of the same kind is equal to
`(n!)/(p!q!r!)`.

Therefore,

Number permutation for the word "COMMTTEE" will be equal to
`(8!)/(2!2!2!)`.

Now,

`(8!)/(2!2!2!)= (8*7*6*5*4*3*2*1)/(2*2*2) =8*7*6*5*3 = 5040`