How many $3$ letter words can be formed from the word "$TESTBOOK$" ?
Letters in this word are : $T,E,S,B,O,K$
- Make a $3$ letter word from $6$ distinct => $P(6,3) = 120$ ways
- Now, Make a $3$ letter word from repeating letters => $C(2,1) * C(3,2) * C(5,1) = 30$ ways
Total $3$ letter words = $150$
Am I right here or missing any possibility ?
Best Answer
Hint -
For second case take repeating letters as group. So we have 2 groups and 4 distinct alphabets.
Pick 1 from group and 1 from 4 distinct letters.