Question

3. A bag of laundry has 20 black socks, 15 blue socks, 12 gray socks, 18 white socks and 10 brown socks. How many socks would you have to pick to guarantee you had:

a. 6 of the same color?    b. 6 gray socks?

Answer 1

20 black, 15 blue, 12 gray, 18 white and 10 brown

a) 6 of the same color: In such questions we take the worst case possible to make sure we have the required results guaranteed. We need 6 of the same color so we assume that we get 5-5 of each color first (that's the worst case) and as soon as we picked the next one we will have 6 of the same color.

So, total socks = 5*5 + 1 = 26

b) 6 gray socks: Again worst case is we get all the other socks then we are getting 6th gray at the end.

So, total socks = 20 + 15 + 18 + 10 + 6 = 69

These are the answer. Please comment if any doubt. Thank you.