Statistics question?

Question

Can some one explain to me how to do it? And what the correct answer was?

A class has 24 boy and 22 girls.

1. What is the probability that 2 boys or 2 girls are chosen at random from the class?
2. What is the probability that the best three students in the class are in the order of boy, girls and girls?

Answer 1

2 boys: 24*23/(46*45) = 26.8%
2 girls: 22*21/(46*45) = 22.3%

24*22*21/(46*45*44) = 12.2%

Answer 2

There are 46 kids in all so there are 46C2 = 46*45/2 = 1,035 ways of choosing 2 kids at random.

There are 24C2 = 24*23/2 = 276 ways of choosing 2 boys from the group.

There are 22C2 = 22*21/2 = 231 ways of choosing 2 girls from the group.

So the probability of selecting either 2 boys or 2 girls is

(276 + 231)/1035 = 48.99%

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The number of ways of selecting 1 boys and 2 girls from the group in the proper order is 24C1 ways of selecting the first boy then 22C2 = 231 ways of selecting the next 2 girls for a total of 24*231 = 5,544 ways.

There are 46C3 = 46*45*44/(3*2) = 15,180 ways of selecting 3 kids at random.

So the probability is 5,544/15,180 = 36.52%

Answer 3

1) I assume that 2 students are being selected.
There are C(46,2) ways of choosing two students out of 46.
There are C(24,2) ways of choosing two boys, C(22,2) ways of choosing 2 girls.
P(2 boys) = C(24,2) / C(46,2) = 4/15
P(2 girls) = C(22,2) / C(46,2) = 77/345
P(2 boys or 2 girls) = sum of above = 169/345 = 0.49

Answer 4

for ur 1st answer.. the numbr of ways u can select 2 boys and 2 gilrs from the grp is as follows.

24c2 * 22c2