+0

# Probability

0
66
2

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?

Oct 22, 2022

#1
+2448
+1

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 $${196 \over 252} = \color{brown}\boxed{7 \over 9}$$

Oct 22, 2022
#2
0