# 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 !

#### Math Olympiad Program

Math Olympiad is the greatest and most challenging academic contest for school students. Brilliant school students from over 100 countries participate in it every year. Cheenta works with small groups of gifted students through an intense training program. It is a deeply personalized journey toward intellectual prowess and technical sophistication.

Google