5 A team of competitive computer programmers have 3 males an

5. A team of competitive computer programmers have 3 males and 3 females who are all equally skilled, and de- cide to assign teams at random.

(a) How many ways are there for a team of two to be all male?

(b) How many ways are there for a team of two to be one male, and one female?

(c) How many ways are there to create a team of two total?

(d) What is the probability that there are an equal num- ber of males and females on a two person team?

Solution

a) Ways of selecting 2 males from 3 is 3C2= 3
b) Ways of selecting 1 male from 3 and 1 female from 3= 3C1*3C1= 3*3=9
c) Selecting 2 from 6= 6C2 = 15
d) total ways of 2 member team -15
  equale number ofmale and female team = 9
Probability = 9/15= 3/5 = .6