Multiple choice

Find the number of permutations which can be formed out of the letters of the word $series$ taken three together?

  1. $32$
  2. $36$
  3. $42$
  4. $46$
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C Correct answer
Explanation

The word 'series' has 6 letters: s, e, r, i, e, s. The distinct letters are s, e, r, i. Since we need to pick 3 letters, we can have cases with repeated letters (s, s, e, e) or all distinct. Calculating permutations for these combinations yields 42.

AI explanation

The word series has 6 letters where s is repeated 2 times and e is repeated 2 times, alongside r and i. To find permutations of 3 letters taken together, we use combinations of cases: all 3 letters different, 2 identical and 1 different, or 2 pairs of identical and 1 different, but the valid cases here are all distinct or exactly one pair. The number of permutations with all distinct letters chosen from s, e, r, i is 4P3 = 24; for two s's and one other letter, the ways are 3C1 x (3! divided by 2!) = 9; for two e's and one other letter, the ways are similarly 3C1 x 3 = 9. Adding these gives 24 + 9 + 9 = 42.

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