Multiple choice

In how many distinct ways can the letters of the word 'CRICKET' be rearranged?

  1. 5040

  2. 2520

  3. 720

  4. 1440

  5. 10080
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Box 1: 16 balls total, 2 blue. Box 2: 5 + x balls total, x blue. P(Blue) = 0.5 * (2/16) + 0.5 * (x / (5+x)) >= 0.25. 1/16 + x / (2(5+x)) >= 0.25. x / (2(5+x)) >= 0.25 - 0.0625 = 0.1875. x / (5+x) >= 0.375. x >= 0.375(5+x) = 1.875 + 0.375x. 0.625x >= 1.875. x >= 3.

AI explanation

The word CRICKET contains seven letters, with the letter C repeated twice. The formula for the permutation of a multiset is n! / p!, where n is the total number of items and p is the frequency of the repeated item. Substituting the values gives 7! / 2! = 5040 / 2 = 2520.

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