If you have eight pairs of socks, each pair a different color, find the probability that if you?

Question

If you have eight pairs of socks, each pair a different color, find the probability that if you
randomly lose five socks, the remaining socks form exactly four matching pairs (and three
unmatched socks).

Answer 1

1. Brown
2. White
3. Blue
4. Green
5. Red
6. Purple
7. Black
8. Yellow

You loss both yellow socks, and one black, purple and red.
Now you have Brown, While, Blue, and Green matched left and a single red, purple, and black sock left.

Answer 2

out of 8 pairs of socks u have to choose 4 pairs(colors) to remain -8C4

then from the other 4 pairs u have to pick 3 different colors to be the part of "unmatched socks"-(4C3)

now,from each of the 3colors that u just picked,get 1 sock from each pair to make up " the three
unmatched socks" -thats 2C1 from each of the 3 colors.

so the total number of ways that "the remaining socks form exactly four matching pairs (and three
unmatched socks)." is

(8C4)(4C3)(2C1)


the total number of ways of having 11 socks remain(same as losing 5) from a total number 16 is 16C11.

so required probability=(8C4)(4C3)(2C1)/16C11