Question

In how many ways can be letter of the word TABLE be arranged so that the vowels are always (1)together (2) separated​

Answer 1

Total no. of vowels in TABLE = 2

Total no. of consonants in TABLE = 3

Here all the vowels and consonants are distinct.

If the vowels are together considered as a single object, then there'll be 4 letters in the word.

Then the no. of arrangements in which vowels are together is,

4 × 3! × 2! = 48

Total no. of possible arrangements with no condition = 5! = 120

Then, the required no. of arrangements in which vowels are separated = 120 - 48 = 72