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

Given

3 Blue, 3 red and 4 green and we have to select 8

Now wwe consider one by one each case and compute the way possible in that case at we sum of them and get total number of possible ways.

(Blue, Red, green) denotes the number of sock in particular case of particular colour.

1) (3,3,2)=8!/3!*3!*2!=40320/72=560

+

2) (3,2,3)=8!/3!*2!*3!=40320/72=560

+

3) (3,1,4)=8!/3!*4!=40320/144=280

+

4) (2,3,3)=8!/2!*3!*3!=40320/72=560

+

5) (2,2,4)=8!/2!*2!*4!=40320/96=420

+

6) (1,3,4)=8!/1!*3!*4!=40320/144=280

Hance,

the total number of ways are= (1)+(2)+(3)+(4)+(5)+(6)

=560+560+280+560+420+280

=2660 (Answer).