Problem of the Week

Problem 33

Congratulations to all Year 11s for finishing your GCSE exams! As a break, this is an easier problem, which will be followed by a harder one next week as a send-off for summer for those who are interested in solving more over the holidays.

Steph has a drawer that contains 8 red socks, 10 blue socks and 12 yellow socks.

A pair of socks denotes 2 socks of the same colour, socks of the same colour are perfectly identical, so there is no difference between socks for the left foot and socks for the right foot.

ai) Assuming Steph picks out socks randomly from her drawer, what is the minimum amount of socks she needs to pick up before she has one pair of socks?

aii) Steph has another drawer that contains socks of different colours. Can you find a generic solution for n different colours? (Assuming each colour has more than 2 socks.)

b)What is the probability that Steph gets a pair of socks within the first 2 socks she picks out from the drawer?

Submit a solution!

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