These are three questions on the subject of basic probability. I have answers, could you please check them?

A bag contains 12 sweets of which 5 are red, 4 are green and 3 are yellow.

A boy chooses 3 of these sweets at random without replacement. Find the probability that

(a) he chooses 3 red sweets, [2]

(b) he chooses no red sweets, [2]

(c) he chooses 1 sweet of each colour. [3]

An A-level Mathematics class contains 5 boys and 6 girls. The teacher is told that 3 members of the class can go to a special lecture and she decides to select these 3 members at random. Find the probability that

(a) 2 boys and 1 girl are selected, [3]

(b) the 3 members selected are all of the same gender. [4]

Two unbiased cubical dice are thrown simultaneously. Calculate the probability that

(a) the score on each die is at least 3, [3]

(b) the scores on the two dice differ by 3. [3]

1]

(a) 5/12 x 4/11 x 3/10 = 60/1320 --> 1/22

(b) 7/12 x 6/11 x 5/10 = 210/1320 --> 7/44

(c) 5/12 x 4/11 x 3/10 = 1/22 [there are six different ways of doing this, so 1/22 x 6 = 6/22, or 3/11]

2]

(a) 5/11 x 4/10 x 6/9 = 12/99 --> 4/33 [again, there are six different ways so 6 x 4/33 = 24/33]

(b) 5/11 x 4/10 x 3/9 = 6/99 --> 2/33

and 6/11 x 5/10 x 4/9 = 4/33

so 2/33 + 4/33 = 6/33

3]

(a) 4/6 x 4/6 = 16/36 --> 4/9

(b) 6/36 --> 1/6

Thank you if you can help it is greatly appreciated.