CAIE A-Level Mathematics 5.3.1 Permutations & combinations

Practise finding probabilities by counting equally likely outcomes with combinations, arrangements and simple enumeration.

Exam points

form probability fractions from favourable arrangements over total arrangements
justify random choice methods by checking that elementary outcomes are equally likely

[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 = ] $^{7} \mathrm{C}_{2}$
M1
${ }^{7} \mathrm{C}_{x}$ seen, x=3 or 2.
[Total =] 35+21
M1
Summing two correct scenarios.
56
A1
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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5.3.1—Permutations and combinations question 1