Multiple choice

Directions: Answer the question independently. In how many different ways can 5 identical apples, 5 identical cherries and 10 identical oranges be arranged such that no two oranges are adjacent to each other?

  1. 2757

  2. 2745

  3. 2772

  4. 792
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Arrange the 5 apples and 5 cherries first (10 items total). The number of ways to arrange these is 10! / (5! * 5!) = 252. There are 11 possible slots for the 10 identical oranges. We must choose 10 slots out of 11, which is C(11, 10) = 11. Total ways = 252 * 11 = 2772.

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