Question

In how many ways can 5 red pencils, 6 blue, and 4 white pencils be distributed among 15 students if one does not distinguish among:

a) 750 ways
b) 15 ways
c) 3003 ways
d) 126 ways

Answer 1

The number of ways to distribute the pencils among the students is determined using combinations. In this case, there are 3003 ways to distribute the 5 red pencils, 6 blue pencils, and 4 white pencils among the 15 students. Option C is correct.

Step-by-step explanation:

To solve this problem, we can use the concept of combinations. We have 15 students and we need to distribute the red pencils, blue pencils, and white pencils among them.

Let's consider the red pencils first. We have 5 red pencils and 15 students, so we can choose 5 students to receive the red pencils in C(15, 5) ways.

Similarly, we can choose 6 students out of the remaining 10 for the blue pencils in C(10, 6) ways. Finally, we distribute the 4 white pencils among the remaining 4 students in C(4, 4) ways. To find the total number of ways, we multiply these three combinations: C(15, 5) * C(10, 6) * C(4, 4) = 3003. Therefore, the answer is c) 3003 ways.