Question

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

Answer 1

Answer:

5040

Step-by-step 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 $\frac{n!}{p!q!r!}$.

Therefore,

Number permutation for the word "COMMTTEE" will be equal to  $\frac{8!}{2!2!2!}$.

Now,

$\frac{8!}{2!2!2!}= \frac{8\times7\times6\times5\times4\times3\times2\times1}{2\times2\times2} =8\times7\times6\times5\times3 = 5040$