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STEP Support Programme

Combinatorics

09-S1-Q13

Ordering, expectation, boys and girls in line, C1.

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[STEP I 2009 Question 13 (Mechanics)]

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08-S1-Q13

Married couples sitting at a table, elementary probability, C1.

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[STEP I 2008 Question 13 (Probability and Statistics)]

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97-S1-Q1

10 and 20 pence coins, number of ways, C1.

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[STEP I 1997 Question 1 (Pure)]

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96-S1-Q12

Binomial coefficients, exam scripts, expectation, C1.

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[STEP I 1996 Question 12 (Probability and Statistics)]

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95-S2-Q2

Recurrence relation, proof by induction.

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[STEP II 1995 Question 2 (Pure)]

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93-S1-Q1

Dice, colors, number of ways, C1.

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[STEP I 1993 Question 1 (Pure)]

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91-S3-Q15

Pack of cards, without replacement, identical, elementary probabliity.

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[STEP III 1991 Question 15 (Probability and Statistics)]

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88-S3-Q16

Balls from urns, mean, expectation, variance, sum of random variable, indicator function.

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[STEP III 1988 Question 16 (Probability and Statistics)]

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Spec-S3-Q16

President of the republic, no children, sons and daughters, expectation.

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[STEP III Specimen Question 16 (Probability and Statistics)]

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Useful Links

Underground Mathematics: Selected worked STEP questions

STEP Question database

University of Cambridge Mathematics Faculty: What do we look for?

University of Cambridge Mathematics Faculty: Information about STEP

University of Cambridge Admissions Office: Undergraduate course information for Mathematics

Stephen Siklos' "Advanced Problems in Mathematics" book (external link)

MEI: Worked solutions to STEP questions (external link)

OCR: Exam board information about STEP (external link)

AMSP (Advanced Maths Support programme): Support for University Admission Tests (external link)