A committee of 4 is chosen at random from a group of 5 married couples. What is the probability that the committee includes no two people who are married?

Question

kinggeorge · Answer

I believe this should be given by the formula $$\large {5\cdot 2^4 \over {10 \choose 4}}$$The bottom represents the total number of possibilities, and the top part is got from this reasoning: 

If no two people can be married, then one couple is not represented. Thus, you get 5C1=5. Also, from the remaining 4 couples, you have to choose 1 person from two. There are two options each time you do this. Hence, $2^4$

candyme · Answer

Thank you! this came out to the correct answer!

kinggeorge · Answer

You're welcome