Multiple choice

Four boys picked up 30 mangoes. In how many ways can they divide them, if all mangoes be identical?

  1. 5450

  2. 5453

  3. 5455

  4. 5456
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

This is a stars and bars problem where we distribute 30 identical items into 4 distinct bins. The formula is C(n+k-1, k-1), where n=30 and k=4. This is C(33, 3) = (33 * 32 * 31) / (3 * 2 * 1) = 11 * 16 * 31 = 5456.

AI explanation

Using the method of distributing identical objects into distinct groups, the required formula is (n + r - 1) C (r - 1) where n is the number of mangoes and r is the number of boys. Substituting n = 30 and r = 4 gives 33 C 3. Calculating this yields (33 * 32 * 31) / (3 * 2 * 1) = 5456. The correct result is 5456.

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