Interactive quiz

Combinatorics quiz

18 progressive questions to recognise the counting model and justify each answer.

18 randomly selected questions Pass mark: 70%

Instructions

Questions progress from simple to complex; choices are shuffled. Each correct answer earns one point; after submission every question shows its answer and explanation.

A menu offers 3 main courses and 2 desserts. How many meals with one of each?

Choose one answer

How many three-digit codes exist if 000 and repeated digits are allowed?

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How many three-digit numbers exist if digits may repeat?

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In how many ways can you arrange 4 different books on a shelf?

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You award gold, silver and bronze among 5 athletes. How many distinct podiums?

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Choose a three-person committee from 5 people, with no roles. How many?

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What is 0! and why?

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Choose 3 scoops from 4 flavours; flavours may repeat and order does not matter. How many choices?

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How many distinct anagrams does ANNA have?

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Five different people sit at a round table. Rotations are equivalent but reflections are not. How many seatings?

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How many four-digit codes, with leading zeros allowed, contain at least one 7?

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Five people line up. Anna and Bruno must stand together. How many orders?

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Twelve students play football, 9 basketball and 4 both. How many play at least one?

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Seven distinct objects go into three labelled groups of sizes 2, 3 and 2. How many allocations?

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Using Pascal’s rule, what is C(6,2)=C(5,2)+C(5,1)?

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An urn has 6 red and 4 blue balls. Draw 3 together: what is the probability of exactly 2 red?

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For three sets: |A|=10, |B|=8, |C|=7, pairwise intersections 3, 2, 1, and triple intersection 1. What is |A∪B∪C|?

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Choose 4 students from 7 girls and 5 boys. What is the probability of exactly 3 girls?

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Have you completed the questions?

Submit your 18 answers to receive your score and review.