[Math] How many $3$ letter words can be formed from the word “$TESTBOOK$”

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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.

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