There are 5 different boxes and 7 different balls.All the balls are to be distributed in the 5 boxes placed in a row so that any box can recieve any number of balls.

Kayley Dickson

Kayley Dickson

Answered question

2022-11-05

There are 5 different boxes and 7 different balls.All the balls are to be distributed in the 5 boxes placed in a row so that any box can recieve any number of balls.

Answer & Explanation

ontzeidena8a

ontzeidena8a

Beginner2022-11-06Added 17 answers

If there were now 2 balls, you can break up your decision about where to put the balls by saying, "First I will decide where Ball 1 goes; then I will decide where Ball 2 goes." Each of these two choices are completely independent - whatever box you choose to put Ball 1 in, it doesn't affect which boxes you might put Ball 2 in. So how many pairs of choices
(box for Ball 1, box for Ball 2)
are there? Can you generalize what is going on to 𝑛 balls and 5 boxes? In fact it should not be too hard to find the formula for 𝑛 balls and 𝑘 boxes.
ajumbaretu

ajumbaretu

Beginner2022-11-07Added 3 answers

You can think of this problem as placing 7 people into 5 rooms. Observe that placing the people is the same as giving each of them a sign (or a key) with the room number, when the people are standing in a prior chosen order.

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