Question

PROBLEM 1
Peter has many socks, all the same except that they are in three different colours. He is leaving to catch an early train to go on a business trip, and he does not want to wake his wife, so he packs in the
dark. He needs eleven pairs of socks, each sock in each pair the same colour. How many socks must he take from his drawer to be sure of achieving this?

Answer 1

Answer:

24 socks

Step-by-step explanation:

The given parameters are;

The number of different colors of socks = 3

Therefore, we have the worst case, the first three socks are different colors, since there are three different colors, the fourth socks is first pair in the worst case scenario

After which, every other two socks makes a pair in the worst case process, the number of socks he must take to make sure he has eleven pairs are given by the pairing table

Number of socks 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Number of pairs 0 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11

Therefore, he must take 24 socks to make sue he has 11 pairs of the same color.