Multiple choice

The number of different combinations that can be formed out of the letters of the word 'INFINITE' taken four at a time is

  1. $20$
  2. $22$
  3. $24$
  4. $120$
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B Correct answer
Explanation

The word 'INFINITE' has 8 letters: I(3), N(2), F(1), T(1), E(1). Combinations of 4 letters can be: 3 of one kind + 1 of another (2 cases: I+others), 2 of one kind + 2 of another (1 case: I,N), 2 of one kind + 2 different (3 cases: I,N), or 4 different (4 cases). Summing these yields 22.

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