Question

How many different words can be formed by taking four letters at a time from the letters of the word "MATHEMATICS" ?

• A. 4908
• B. 5216
• C. 2454
• D. 3246

Answer 1

The correct option is C 2454

Here M,A, and T occur twice, rest all words one time.
Three cases possible:-
CASE 1-All the words are different
$8C4\times 4!$
CASE 2:-Two same and two different
$3C1\times 7C2\times \frac{4!}{2!}$
CASE 3:-Two same of 1st kind and two
same of 2nd kind
$3C2\times \frac{4!}{2!\times 2!}$
Answer is (CASE 1+CASE 2+CASE 3) =2454