Question

how many words can be made by using all letters of the word MATHEMATICS in which all vowels are never together. ( Class 11 , permutations and combinations)​

Answer 1

Answer:

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

Step-by-step explanation:

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