# Understand the problem

##### Source of the problem

##### Topic

Combinatorics

##### Difficulty Level

7/10

##### Suggested Book

Enumetarive Combinatorics – ( Problem Solving Strategies ) by Arthur Engel

# Start with hints

# Watch video

# Connected Program at Cheenta

First can you try finding the number of ways in which we can choose the 2 shared elements ? * That would be 5C2 = 10 ways.* Can you try completing this ?

All that remains now is to place the remaining 3 elements into the subsets. In how many ways can we do this ?

**So basically, if we think about it a little, it is equivalent to the problem of placing 3 elements in 4 gaps.** **Evidently, this can be done in 4C3 = 4 ways. ** Now, it’s pretty easy to arrive at the answer…could you do it by yourself ? * *

The final answer can be easily found out using the Multiplication Principle, which leads us to… **4 x 10 = 40 ways **

And, we are done !

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