CAIE A-Level Mathematics A2 5.3.1 Permutations and Combinations Questions

Practise calculating probabilities for arrangements, selections and repeated independent trials.

Exam points

calculate probabilities from equally likely outcomes
use complementary and conditional counting ideas in probability
model repeated trials and events using probability rules

[Maximum number: 4]

Raman and Sanjay are members of a quiz team which has 9 members in total. Two photographs of the quiz team are to be taken.

For the first photograph, the 9 members will stand in a line.

For a random division into a group of 5 and a group of 4, find the probability that Raman and Sanjay are in the same group as each other.

[Number of ways with Raman and Sanjay together on back row = ] $^{7} \mathrm{C}_{3}$
[Number of ways with Raman and Sanjay together on front row = ] $^{7} \mathrm{C}_{2}$ ${ }^{7} \mathrm{C}_{x}$ seen, x=3 or 2.
[Total =] 35+21
Summing two correct scenarios.
56
Evaluated - may be seen used in probability.
If M0 scored, SC B1 for 56 WWW.
Probability $=\frac{\text { their } 56}{\text { their }(c)}=\frac{56}{126}, \frac{4}{9}, 0.444$
B1 FT
FT their 56 from adding 2 or more scenarios in numerator and their (c) or correct as denominator.

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CAIE A-Level Mathematics A2 5.3.1 Permutations and Combinations Questions question 1