IPM Question Paper 2020 | IPM Rohtak Quantitative Aptitude

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Question 8 : Five racquets needs to be placed in three boxes. Each box can hold all the five racquets. In how many ways can the racquets be placed in the boxes so that no box can be empty if all racquets are different but all boxes are identical?

1. 24
2. 25
3. 27
4. 26

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Video Explanation

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Explanatory Answer

Let the 5 racquets be a, b, c, d, e
3 Boxes are Identical
Since the boxes are identical 3 in First box, 1 in Second and 1 in third is not different from 1 in first, 3 in second and 1 in third.

Box 1	Box 2	Box 3
3 racquets 5C3 ways	1 racquets 2C1 ways	1 racquets 1C1 way
2 racquets 5C2 ways	2 racquets 3C2 ways	1 racquets 1C1 way

But there is a catch in the above table.
Imagine this process, after selecting 3 out of a, b, c, d, e
Let's say we select d, e, c. a and b have to be put in two identical boxes.
This can be done only in one way.

In second scenario let's assume a and b in First box and c and d in second box and e in third box. But the possibility will be same when c and d in First box and a and b in second box.
So, it is \\frac{^{5}C_{2} × ^{3}C_{2}}{2}) = 15 ways, In first scenario ⁵C₃ = 10 ways
Totally 25 ways.

The answer is 25

Choice B is the correct answer.

 

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