The problem can be solved using the concept of combinations in combinatorics.

Step 1: Since no box can be empty, we first place one doll in each box. We have 8 dolls, so we can do this in 8 choose 5 ways.

Step 2: Now we have 3 dolls left and 5 boxes. Each doll can go into any of the 5 boxes. So, for each doll, there are 5 choices of boxes. Since there are 3 dolls, the total number of ways is 5^3.

Step 3: Multiply the results from step 1 and step 2 to get the total number of ways the dolls can be packed in the boxes.

So, the answer is (8 choose 5) * 5^3.

Question

The problem can be solved using the concept of combinations in combinatorics.

Step 1: Since no box can be empty, we first place one doll in each box. We have 8 dolls, so we can do this in 8 choose 5 ways.

Step 2: Now we have 3 dolls left and 5 boxes. Each doll can go into any of the 5 boxes. So, for each doll, there are 5 choices of boxes. Since there are 3 dolls, the total number of ways is 5^3.

Step 3: Multiply the results from step 1 and step 2 to get the total number of ways the dolls can be packed in the boxes.

So, the answer is (8 choose 5) * 5^3.

Knowee AI · Accepted Answer

The problem can be solved using the concept of combinations in combinatorics.

Step 1: Since no box can be empty, we first place one doll in each box. We have 8 dolls, so we can do this in 8 choose 5 ways.

Step 2: Now we have 3 dolls left and 5 boxes. Each doll can go into any of the 5 boxes. So, for each doll, there are 5 choices of boxes. Since there are 3 dolls, the total number of ways is 5^3.

Step 3: Multiply the results from step 1 and step 2 to get the total number of ways the dolls can be packed in the boxes.

So, the answer is (8 choose 5) * 5^3.

In how many ways can 8 different dolls be packed in 5 identical gift boxes such that no box is empty if any of the boxes hold all of the toys?

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