SOLUTION: Four girls and eight boys want to be president or vice president of the Student Council. To be fair, a teacher puts their names in a hat and selects two. Find each probability.

Question 295620: Four girls and eight boys want to be president or vice president of the Student Council. To be fair, a teacher puts their names in a hat and selects two. Find each probability.
1. Find the probability that two boys are elected.
2. Find the probability that two girls are elected.
3. find the probability that the president is a boy and the vice president is a girl.
4. Find the probability that the president is a girl nad the vice president is a boy.
My son answered all the questions as 1/6.
Please explain your answers, so I can explain it to my son. Thank you for your time.
Answer by palanisamy(496) (Show Source): You can put this solution on YOUR website!
Four girls and eight boys want to be president or vice president of the Student Council.
A) Out of 8 boys 2 can be selected in 8C2 = (8*7)/(1*2)=28 ways
B) Out of 4 girls 2 can be selected in 4C2 = (4*3)/(1*2)= 6 ways
C) Out of 8 boys 1 can be selected as president in 8C1 = 8 ways and
out of 4 girls 1 can be selected as vice president in 4C1 = 4 ways.
Total number of ways = 8*4 = 32
D) Out of 8 boys 1 can be selected as vice president in 8C1 = 8 ways and
out of 4 girls 1 can be selected as president in 4C1 = 4 ways.
Total number of ways = 4*8 = 32

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