Jack and John and 8 other classmates have participated in a class committee election.The class committee consists of 4 members.If the committee members are randomly selected from the participants, find the probability that either Jack or John is selected.
+118667 Well I am going to interpret this as either John or Jack but not both
The number of ways that 4 people can be chosen from 10 is 10C4
Now split hese 10 people into 2 groups.
Jack and John in the first group and the other 8 people in the 2'nd group.
So we want 1 person from group 1 and 3 from group2
that is 2C1*8C3
therefore P(Jack or john but not both selected)=
$$\dfrac{^2C_1*^8C_3}{^{10}C_4}=\dfrac{2*56}{210}=\dfrac{56}{105}=\dfrac{8}{15}$$
