There are 8 married couples at a party. 6 is chosen at random to win a door prize. what is the probability?

that they are 3 married couples?There are 8 married couples at a party. 6 is chosen at random to win a door prize. what is the probability?
Number of ways of choosing 6 people out of 16 = 16 choose 6


Number of ways of choosing 3 couples out of 8 = 8 choose 3





Thus, probability = (8 choose 3)/(16 choose 6) = 0.007 i.e., pretty slim.There are 8 married couples at a party. 6 is chosen at random to win a door prize. what is the probability?
I assume you mean that:


There are 8 married couples, or 16 people, at a party and 6 individuals are chosen at random.


The probability that the six are three married couples?





Let's pick them in a specific order.


The first pick can be any of 16


The second can only be the 1 spouse


The third can be any of the remaining 14


The fourth can only be the 1 spouse


The fifth can be any of the remaining 12


The six can only be the 1 spouse.


This means 16*14*12 ways, or 2688 to pick three married couples if they are one right after the other.


There are 720 (6!) ways to pick those particular six people.


2688 * 720 = 1935360 ways, and there are (16!)/((16-6)!) to pick ANY six people out of the 16, the probability is 1935360/5765760 or


0.336
8C3/16C6=56/8008