permutation question please help me thank you?

a> There are total 10 socks and we have to choose 2 out of them so the chances are

10 P 2 = 90 ways

b> if a blue comes first then the second one should be white and vice versa so chances are

6*4 + 4*6 = 48

c> if a blue sock comes first then the next must be blue and same for white so

6P2 + 4P2 = 30 +12 =42

Glad to help

(a) altogether 10 socks, so for the first draw there are 10 possibilities, when one sock is taken, then for each of the 10 possibilities you have 9 possibilities left, so it is 10 * 9 = 90

(b) first possibility: first blue sock of 6 then white sock of 4: 6 * 4 = 24

second possibility: first white sock of 4 then blue sock of 6: 4 * 6 = 24

altogether -> 48 possibilities

(c) first possibility: blue sock of 6 then blue sock of 5 (because one was taken): 6 * 5 = 30

second possibility: white sock of 4 then white sock of 3 (guess why?): 4 * 3 = 12

altogether -> 42 possibilities

check if (a) = (b) + (c) : 90 = 48 + 42 (correct)