Multiple choice

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

  1. $^{33}C_3$
  2. $^{33}C_2$
  3. $5456$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Since the mangoes are identical, we can use the stars and bars method to distribute 30 identical items among 4 distinct boys. This is equivalent to finding the number of non-negative integer solutions to x1 + x2 + x3 + x4 = 30, which is given by the combination formula C(n + r - 1, r - 1) = C(30 + 4 - 1, 4 - 1) = C(33, 3).

AI explanation

Distributing 30 identical mangoes among 4 boys such that a boy can receive zero mangoes is a problem of distributing identical items into distinct groups, solved using the stars and bars method. The formula for the number of ways is (n + r - 1) C (r - 1), where n is the number of items and r is the number of groups. Plugging in n = 30 and r = 4 gives (30 + 4 - 1) C (4 - 1), which equals 33C3.

Keep practicing — related questions