A class of 10 students, including Jenny, Kenny, and Lenny, are split into two groups of 5 students at random to work on a group project. What is the probability that both Jenny and Kenny are in a different group?
+2666 There are \({10 \choose 5} = 252\) ways to choose the groups.
If Jenny and Kenny are in the same group, there are 3 spots left, which makes for \({8 \choose 3} = 56\) ways to be in the same group.
So, there are 252 - 56 = 196 ways for Jenny and Kenny to be in different groups.
The probability is then \({196 \over 252} = \color{brown}\boxed{7 \over 9}\)
