Question

You have brown, pink, black, and white socks in a drawer (8 of each color). In each of the following cases, what is the minimum number that you must take out to ensure that:

a) You have a matching pair?

b) You have two of different colors?

c) You have at least 3 brown or 4 pink or 5 black or 7 white socks?

Answer 1

a) matching pair:

Let's say you've picked four socks( since we have four colors). If you've already found a pair after two or three or four draws, you're done.

But it's possible after four draws that you haven't drawn a match yet:

So assume you don't have that pair after drawing 4 socks: that is, you have one brown, one pink, one black and one white sock.

therefore the fifth sock you pick must be one of the given 4 colors. That is it must be either the brown, pink, black or white sock you've already picked.

Hence the answer is 5.

b) two different colors:

as you have 8 numbers of each color, taking in to consideration fot the worst case that you got 8 socks of same color in the first pic. Then the second pic would of one would give the two different color.

Therefore the answer is 9.

c) at least 3 brown or 4 pink or 5 black or 7 white socks

here worst case occurs when all are equally picked

1)    brown, pink, black,white--->(2,2,2,2) =8 (do not meet any criteria ,minimum is 3 browns) sp pic next socks and in worst case it might be any color other than brown

2)   brown, pink, black,white--->(2,3,2,2) or

brown, pink, black,white--->(2,2,3,2) or  brown, pink, black,white--->(2,2,2,3)

3) it continues till each get thrshold i.e

brown, pink, black,white--->(2,3,4,6)

at this point one more socks will results into our criteria so

brown, pink, black,white--->(2,3,4,6) + 1 = 16;

the answer is 16