Statistics & probability · SS3

Counting

Counting arrangements and selections without listing them all: permutations and combinations.

Before this: Probability
Leads to: Permutation & combination

Learn

1Arrangements and selectionsCounting without listing: the multiplication rule, factorials, permutations (order matters) and combinations (order doesn't), repeated letters, and committees.Done18 min

Practise

Answer counting questions one at a time. You'll know straight away whether you're right, with hints and the working step by step.

Your progress is saved on this device as you practise. No account needed.

Start practising

Past questions (24)

From 1992–2018: 24 JAMB. Theory questions first, then objective, newest first.

Objective (24)

JAMB 2018 · UTME · Q27In how many ways can 6 subjects be selected from 10 subjects for an examination?
JAMB 2017 · UTME (set 2) · Q45In how many ways can the letters of the word ACCEPTANCE be arranged?
JAMB 2016 · UTME · Q18In how many ways can a delegation of 3 be chosen from 5 men and 3 women, if at least 1 man and 1 woman must be included?
JAMB 2014 · UTME · Q48In how many ways can a team of 3 girls be selected from 7 girls?
JAMB 2013 · UTME · Q47In how many ways can a student select 2 subjects from 5 subjects?
JAMB 2013 · UTME · Q48In how many ways can 3 seats be occupied if 5 people are willing to sit?
JAMB 2012 · UTME · Q47Evaluate ${}^{n + 1}C_{n - 2}$ if $n = 15$ .
JAMB 2012 · UTME · Q48In how many ways can the letters of the word TOTALITY be arranged?
JAMB 2011 · UTME · Q11Rahila has 7 different posters to be hung in her bedroom, living room and kitchen. Assuming she plans to place a poster in each of the 3 rooms, …
JAMB 2011 · UTME · Q47In how many ways can the letters of the word ELATION be arranged?
JAMB 2011 · UTME · Q48In how many ways can five people sit round a circular table?
JAMB 2010 · UTME · Q49In how many ways can a committee of 2 women and 3 men be chosen from 6 men and 5 women?
JAMB 2004 · UME · Q46In how many ways can 2 students be selected from a group of 5 students in a debating competition?
JAMB 2004 · UME · Q47A committee of six is to be formed by a state governor from nine state commissioners and three members of the state house of assembly. In how …
JAMB 2003 · UME · Q47If $^nP_3 - 6\,(^nC_4) = 0$ , find the value of $n$ .
JAMB 2003 · UME · Q49Find the number of committees of three that can be formed consisting of two men and one woman from four men and three women.
JAMB 2002 · UME · Q28How many three-digit numbers can be formed from 32564 without any digit being repeated?
JAMB 2001 · UME · Q47Find the number of ways of selecting 8 subjects from 12 subjects for an examination.
JAMB 2001 · UME · Q48If $^6P_r = 6$ , find the value of $^6P_{r + 1}$ .
JAMB 2000 · UME · Q43In how many ways can the word MATHEMATICS be arranged?
JAMB 2000 · UME · Q49In how many ways can a delegation of 3 be chosen from among 5 men and 3 women, if at least one man and at least one woman must be included?
JAMB 1999 · UME · Q43If $\dfrac{^6C_r}{^6P_r} = \frac16$ , find the value of $r$ .
JAMB 1992 · UME · Q49Five people are to be arranged in a row for a group photograph. How many arrangements are there if a married couple in the group insist on sitting …
JAMB 1992 · UME · Q50A student has 5 courses to take from Mathematics and Physics. There are 4 courses in Mathematics and 3 in Physics which he can choose from at …