Q:

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

Accepted Solution

A:
Answer:5040Step-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 [tex]\frac{n!}{p!q!r!}[/tex].Therefore, Number permutation for the word "COMMTTEE" will be equal to  [tex]\frac{8!}{2!2!2!}[/tex].Now, [tex]\frac{8!}{2!2!2!}= \frac{8\times7\times6\times5\times4\times3\times2\times1}{2\times2\times2} =8\times7\times6\times5\times3 = 5040[/tex]