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Answer:
1260 ways
Step-by-step explanation:
Given
[tex]Dolls = 8[/tex]
[tex]Boxes = 5[/tex]
From the question, we understand that: the boxes are identical; however, the dolls are different.
Since no box can be empty, the following scenario exists:
2, 2, 2, 1, 1
This means that 3 of the 5 boxes will hold 2 dolls each while the other 2 will hold 1 doll each.
So, the number of selection is as follows:
2 of the 8 dolls will be selected in 8C2 ways
2 of the remaining 6 dolls will be selected in 6C2 ways
2 of the remaining 4 dolls will be selected in 4C2 ways
1 of the remaining 2 will be selected in 1C1 ways
1 of the remaining 1 will be selected in 1C1 ways
[tex]Expression: ^8C_2 * ^6C_2 * ^4C_2 * ^1C_1 * ^1C_1[/tex]
Since the boxes are identical, we have to divide the above expression by 2 to get the number of ways:
[tex]Ways = \frac{^8C_2 * ^6C_2 * ^4C_2 * ^1C_1 * ^1C_1}{2}[/tex]
[tex]Ways = \frac{28 * 15* 6* 1 * 1}{2}[/tex]
[tex]Ways = \frac{2520}{2}[/tex]
[tex]Ways = 1260[/tex]