Class 11

Math

Algebra

Permutations and Combinations

How Many words, with or without meaning, each of $2$ vowels and $3$ consonants can be formed from the letters of the word $DAUGHTER$?

Total vowels $=3$ and consonants $=5$

Now we have to make a word using five letters from given word.

Here we have to choose $2$ out of three vowels and $3$ out of $5$ consonants which can further be arranged in $5!$ ways.

$_{3}C_{2}×_{5}C_{3}×5!$