Question

In how

many ways can the letters of the word TABLE be arranged
so that the vowels are always together and seperated​

Answer 1

48 ways

Explanation:

Treat the vowels as 1 unit by itself which in this case is A & E.

Imagine filling in 4 slots:

_ _ _ _ , since A&E are treated as 1 letter.

Thus we have 4 ways to fill in 1st slot, 3 ways for 2nd, 2 for 3rd and 1 for last.

which makes 4 * 3 * 2 * 1 = 24.

However, do note A&E can be arranged as AE or EA meaning,

we need to multiply by 2 factorial.

24 * 2 = 48