Question

A sock drawer contains three blue socks, three red socks, and four green socks. A spider pulls out eight of the socks and puts them on her eight feet. In how many ways can this happen? (Her feet are distinct so the order of the socks matters, but socks of the same color are indistinguishable. For instance, one way is RRBGGBRG.)

Answer 1

number of ways to arrange 1 blue ; 3 red and 4 green socks=8!/(1!*3!*4!) =280

number of ways to arrange 2 blue ; 3 red and 3 green socks=8!/(2!*3!*3!) =560

number of ways to arrange 2 blue ; 2 red and 4 green socks=8!/(2!*3!*4!) =420

number of ways to arrange 3 blue ; 3 red and 2 green socks=8!/(3!*3!*2!) =560

number of ways to arrange 3 blue ; 2 red and 3 green socks=8!/(3!*2!*3!) =560

number of ways to arrange 3 blue ; 1 red and 4 green socks=8!/(3!*1!*4!) =280

total number of ways =280+560+420+560+560+280 =2660