Question

In how many different ways can the letters of the word mathematics permutations be arranged which vowels are come together

Answer 1

Answer:

In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together? In the word 'MATHEMATICS', we'll consider all the vowels AEAI together as one letter. Thus, we have MTHMTCS (AEAI). Number of ways of arranging these letters =8! / ((2!)

✌✌✌✌✌✌✌✌✌✌✌✌✌✌✌✌

Answer 2

When the vowels OIA are always together, they can be supposed to form one letter. Then, we have to arrange the letters PTCL (OIA). Now, 5 letters can be arranged in 5! = 120 ways.