TopicFurther Maths
Statistics & probability · SS2
Permutation & combination
Permutations and combinations, including arrangements with restrictions.
- Before this
- Counting
- Leads to
- Probability & distributions
Learn
- 1Equations and harder arrangementsSolve equations in ⁿPᵣ and ⁿCᵣ, arrange objects that must stay together or letters that repeat, and count numbers made from given digits under conditions.Done21 min
- 2Committees with conditions and probabilityCommittees with 'at least', 'at most', a particular person in or out, and people who can't serve together; splitting people into groups; and probabilities found by counting selections.Done22 min
Flashcards
12 cards: the rules, facts and methods to know by heart, with the diagrams from the lessons. They come back until you know them.
Practise
Answer permutation & combination 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.
Past questions (43)
From 2008–2023: 40 WAEC, 3 NECO. Theory questions first, then objective, newest first.
Theory (35)
- NECO 2023 · Paper 2 · Q5From 10 male and 8 female staff in a school, a committee of 5 men and 3 women is to be set up. In how many ways can this be done if:
- WAEC 2023 · Paper 2 · Q1Given that , find the value of .
- WAEC 2022 · Paper 2 · Q12A basket contains 12 fruits: orange, apple and avocado pear, all of the same size. The numbers of oranges, apples and avocado pears form three …
- WAEC 2022 · Paper 2 · Q9Given that , and are the first 3 terms of a linear sequence (A.P.), find the:
- WAEC 2019 · Paper 2 · Q1Given that , simplify .
- WAEC 2019 · Paper 2 · Q13In a bakery, of loaves of bread produced are of bad quality. If twelve loaves are selected at random from the bakery, calculate, correct …
- WAEC 2019 · Paper 2 · Q1How many even numbers greater than 5000 can be formed using the digits 1, 2, 4, 5, 6 if no digit is used more than once?
- WAEC 2019 · Paper 2 · Q13A fair coin is tossed 6 times. Calculate the probability of obtaining at most three heads.
- WAEC 2018 · Paper 2 · Q6The probability that Kunle solves a particular question is while that of Tayo is . If both of them attempt the question, find …
- WAEC 2018 · Paper 2 · Q13At the end of full time, a football match between teams and was goalless. The winning team had to be decided through penalty kicks. Each …
- WAEC 2018 · Paper 2 · Q12| Candidate | A | B | C | D | E | F | G | H | I | J |
- WAEC 2018 · Paper 2 · Q5A basket contains 4 ripe oranges, 3 unripe oranges and 5 bananas. In how many ways can:
- WAEC 2017 · Paper 2 · Q13A bag contains 10 identical balls of which 3 are black and the rest brown. Two balls are drawn at random one after the other from the bag without …
- WAEC 2017 · Paper 2 · Q5A committee of 5 members is to be formed from 6 men and 7 women. Calculate the probability that it consists of:
- WAEC 2016 · Paper 2 · Q11If , find the value of .
- WAEC 2016 · Paper 2 · Q13Two different Mathematics books, 5 different Physics books and 3 different Chemistry books are to be arranged on a shelf. How many arrangements …
- WAEC 2016 · Paper 2 · Q5If , find the value of .
- WAEC 2014 · Paper 2 · Q6A committee of 3 is formed from a panel of 5 men and 3 women. Find the:
- WAEC 2013 · Paper 2 · Q15The probability that a man wins a race is 0.8. In four different races, what is the probability that he wins: (i) all races; (ii) no race; (iii) …
- WAEC 2013 · Paper 2 · Q5Three school prefects are to be chosen from four girls and five boys. What is the probability that:
- WAEC 2013 · Paper 2 · Q13A committee of 6 is to be selected at random from a group of 7 boys and 4 girls. (i) In how many ways can this be done if there are no restrictions? …
- WAEC 2013 · Paper 2 · Q6Simplify .
- WAEC 2012 · Paper 2 · Q15A class consists of 6 girls and 10 boys. If a committee of 3 is chosen at random from the class, find the probability that:
- WAEC 2011 · Paper 2 · Q6Evaluate , correct to two decimal places.
- WAEC 2011 · Paper 2 · Q13A committee of five is to be formed among 6 Ghanaians, 8 Nigerians and 5 Gambians. In how many ways can the committee be formed if: (i) there …
- WAEC 2010 · Paper 2 · Q14A box contains 3 white and 5 green identical balls. Another box contains 6 white and 4 green identical balls. A ball is drawn at random …
- WAEC 2010 · Paper 2 · Q15A team of 3 students is to be selected from 5 boys and 4 girls to represent a school in a quiz. (i) If there is no restriction, in how many ways …
- WAEC 2010 · Paper 2 · Q5A committee of four persons is to be formed from 7 girls and 5 boys. Calculate, correct to two decimal places, the probability that the committee …
- WAEC 2009 · Paper 2 · Q13Simplify .
- WAEC 2009 · Paper 2 · Q6A student representative council consists of 8 girls and 6 boys. If an editorial board of 5 persons is to be formed, what is the probability …
- WAEC 2009 · Paper 2 · Q13If , find .
- WAEC 2009 · Paper 2 · Q15In a test, eight students obtained the following marks in Biology and Physics.
- WAEC 2008 · Paper 2 · Q15Five (5) female and seven (7) male teachers applied for 4 vacancies in a Junior High School. The teachers are equally qualified. Find the number …
- WAEC 2008 · Paper 2 · Q14(i) In how many ways can eight boys be seated in a row? (ii) If two of the boys in (a)(i) cannot sit together, in how many ways can they be seated?
- WAEC 2008 · Paper 2 · Q15Simplify .
Objective (8)
- NECO 2023 · Paper 1 · Q30In how many ways can 10 people be seated at a round table if there is no restriction?
- NECO 2023 · Paper 1 · Q43In how many ways can a committee of eight councillors be selected from ten councillors in a Local Government?
- WAEC 2023 · Paper 1 · Q20In how many ways can four Mathematicians be selected from six?
- WAEC 2023 · Paper 1 · Q6In how many ways can a committee of 3 women and 2 men be chosen from a group of 7 men and 5 women?
- WAEC 2022 · Paper 1 · Q13Evaluate: .
- WAEC 2022 · Paper 1 · Q18In how many ways can six persons be paired?
- WAEC 2020 · Paper 1 · Q26In how many ways can the letters of the word MEMBER be arranged?
- WAEC 2020 · Paper 1 · Q32A three-digit odd number less than 500 is to be formed from 1, 2, 3, 4 and 5. If repetition of digits is allowed, in how many ways can this be …