Class 11

Math

Algebra

Permutations and Combinations

How many words can be formed from the letters of the word 'DAUGHTER' so that the vowels always come together?

- $720$
- $2160$
- $4320$
- None of these

Take all the vowels A U E together and take them as one letter.

Then, the letters to be arranged are D, G, H, T, R, (A U E).

These $6$ letters can be arranged in $6$ places in $6!$ ways.

Now, $3$ letters A, U, E among themselves can be arranged in $3!=6$ ways.

$∴$ required number of words $=(6!)×6=(6×5×4×3×2×1×6)=4320$.