CAIE A-Level Mathematics 5.2.1 Permutations & Combinations

Practise choosing permutations or combinations and splitting constrained selections into complete, non-overlapping cases.

Exam points

choose nPr when order or assigned roles matter and nCr for unordered selections
split at-least, at-most or exact restrictions into exhaustive selection cases
select several labelled groups in stages while updating the remaining pool

[Maximum number: 2]

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 the second photograph, the members will stand in two rows, with 5 in the back row and 4 in the front row.

In how many different ways can the 9 members be divided into a group of 5 and a group of 4?

${ }^{9} \mathrm{C}_{5}\left[\times{ }^{4} \mathrm{C}_{4}\right]$
M1
${ }^{9} \mathrm{C}_{x}\left[\times^{9-x} \mathrm{C}_{9-x}\right] x=4$ , 5. Condone $\times 1$ for ${ }^{9-x} \mathrm{C}_{9-x}$ .
Condone use of P .
126
A1
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5.2.1—Permutations and combinations question 1