Question

How many ways are there to put 5 balls in 3 boxes if the balls are not distinguishable but the boxes are

Answer 1

Answer: 5

Here are some ways:

• 1 ball, 2 balls, 2 balls
• 2 balls, 1 ball, 2 balls
• 3 balls, 1 ball, 1 ball
• 1 ball, 3 balls, 1 ball
• 1 ball, 1 ball, 3 balls

Hope this helps!

Answer 2

Answer:

10 ways

Step-by-step explanation:

Since the boxes are not distinguishable, the order doesn't matter in this case. Therefore, the answer would be 5 choose 3, which is $\frac{5!}{2!3!} = \frac{5*4*3*2}{2*3*2} = 10$