Understand the problem
Source of the problem
Enumetarive Combinatorics – ( Problem Solving Strategies ) by Arthur Engel
Start with hints
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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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