Question

In how many ways can we put five identical fruits into three bowls? Note that the bowls may be empty.

A) 10
B) 15
C) 20
D) 5

Answer 1

In 20 ways we can put five identical fruits into three bowls

Therefore, correct answer is C) 20

Step-by-step explanation:

To determine the number of ways to distribute five identical fruits into three bowls (where the bowls may be empty), we can use the concept of stars and bars. Imagine each fruit as a star, and the bowls as dividers (bars) between them. This forms a visual representation of the distribution. In this scenario, we have five stars (fruits) and two bars (dividers) for three bowls. The formula for distributing n identical items into k distinct containers is (n+k-1) choose (k-1). Applying this formula, we get (5+3-1) choose (3-1) = 7 choose 2 = 7! / (2! x 5!) = 21 / 2 = 10 ways.

The stars and bars method is a combinatorial technique used to solve problems related to distributing indistinguishable objects into distinct containers. It finds applications in various mathematical and computational scenarios, providing an efficient way to analyze and solve problems related to distribution and partitioning.

Therefore, correct answer is C) 20