Math, asked by yashjaiswar0709, 4 months ago

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 boxs hold all of the toys?​

Answers

Answered by amitnrw
3

Given : 8 different dolls to  be packed in 5 identical gift boxes

To Find : Number of ways if no box is empty

Step-by-step explanation:

5 identical gift box

Hence there are 3 ways numbers of dolls allocations are as boxes are identical.

Box         Box            Box       Box        Box   ( 5 Boxes)

4               1                1              1              1

3               2               1              1              1

2               2               2              1             1

Box1     Box2       Box3     Box 4      Box 5

4               1                1              1              1

Ways = ⁸C₄.⁴C₁.³C₁.²C₁  / 4! = 70   as 4 boxes are identical

Box1     Box2       Box3     Box 4      Box 5

3               2               1              1              1  

Ways = ⁸C₃.⁵C₂.³C₁.²C₁/3!= 560   as 3 boxes are identical

Box1     Box2       Box3     Box 4      Box 5

2               2               2              1             1

Ways = ⁸C₂.⁶C₂.⁴C₂.²C₁/3!.2! = 420   ( as 3 boxes and 2 boxes are identical)

Total Ways =70 + 560 + 420

= 1050

There are  1050 ways in which 8 different dolls be packed in 5 identical gift boxes such that no box is empty

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