TMUA Permutations and Combinations
TMUA doesn't tend to test on this topic directly, unlike many college entrance exams, though of course it indirectly tests it in areas such as binomial expansion coefficients etc (see that topic for question examples).
For those so interested, we offer both one to one TMUA coaching on permutations and combinations, as well as online group coaching via Zoom - 'TMUA Prerequisite Maths Two' is Session #2 of 20. Check our TMUA Group Coaching Schedule page for dates when these sessions are available - details of what we cover in each group session can be found on our TMUA Coaching Sessions Overview page. For more general information on our online sessions check out our 'Online Coaching FAQ'.
Feel free to contact us if you require more information regarding any of the above.
Free Revision Resources
The below list of questions links to short videos (teasers) on our YouTube channel which directly or indirectly test elements of what is required to succeed in answering TMUA questions on permutations and combinations - they also provide a detailed solution to the question posed, together with tips and tricks and are arranged roughly in increasing order of difficulty. All the videos are taken from the Gresty Academy YouTube podcast 'A Crash Course in TMUA Must Know Maths' which contains hundreds of TMUA style questions and is great for revision.
- Teaser #375 - tests ability to calculate basic permutations in a 'balls in bag' game - Standard
- Teaser #97 - tests understanding of probability two balls picked are different colours given ratios of balls in bag - Standard
- Teaser #9 - tests ability to count number of ways of arranging people in a circle given constraints - Standard
- Teaser #109 - tests ability to find probability a girl sits between her friends - Standard
- Teaser #331 - tests ability to enter data into a Venn Diagram and work out a probability using basic combinatorics - Medium
- Teaser #505 - tests ability to find the coefficient where powers of a and b are the same in a binomial expansion - Medium
- Teaser #101 - tests counting arrangements of a word with restrictions - Medium
- Teaser #63 - tests ability to count number of integer solutions to xyz=360 - Medium
- Teaser #155 - tests how to arrange 3 families of 4 at the cinema - Medium
- Teaser #220 - test how to calculate probability exactly 2 people from 10 have a birthday today (calculation too hard for TMUA but method useful) - Medium
- Weekend Workout #20 - tests knowledge of permutations of balls in a row - Medium
- Teaser #443 - tests how to count a specific number of perfect square factors of a number - Quite Tough
- Teaser #279 - tests knowledge of a useful trick to find coefficient of x^3 in a binomial expansion - Quite Tough
TMUA Past Questions on Permutations and Combinations: SP p2 q13; 2017 p2 q20; 2023 p1 q6
Practice makes perfect - good luck in your studies!