Question

The number of words that can be formed by using the letters of the word mathematics that start as well as end with t is

Answer 1

Answer:

Required number of words = (10080 x 12) = 120960

Step-by-step explanation:

In the word 'MATHEMATICS', we'll consider all the vowels AEAI together as one letter.

Thus, we have MTHMTCS (AEAI).

Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice

 Number of ways of arranging these letters =8! / ((2!)(2!))= 10080.

Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.

Number of ways of arranging these letters =4! / 2!= 12.

 Required number of words = (10080 x 12) = 120960