# Exam-Style Question on Combinatorics

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 678. This question is similar to one that appeared on an IB AA Higher paper in 2023. The use of a calculator is allowed.

A fund-raising activity involves people choosing three balls from a jar containing balls numbered 1 to 30. A prize of £5 is awarded if the three numbers chosen sum to a multiple of three. It costs £2 to have a go.

(a) How many ways are there of choosing three numbers from the integers 1 to 30 that sum to a multiple of 3?

(b) What is the probability of person winning a prize?

(c) What is the expected profit made for the fund after 300 people have had a go?

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