O-LevelAdditional MathematicsPermutations and combinations4037/12 · Oct/Nov 2014 · Q109 Marks

Find how many different 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5 and 6 if no digit is repeated.

(a)(i)Find how many different 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5 and 6 if no digit is repeated.[1]
(a)(ii)How many of the 4-digit numbers found in part (i) are greater than 6000?[1]
(a)(iii)How many of the 4-digit numbers found in part (i) are greater than 6000 and are odd?[1]
(b)(i)Find the number of different teams that can be chosen if the team has to have equal numbers of girls and boys.[3]
(b)(ii)Find the number of different teams that can be chosen if the team has to include the youngest and oldest boy and the youngest and oldest girl.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2014). The mark or mark type is shown in brackets.

[1] B1 360
[1] B1 60
[1] B1 36
[2] B1 for 8C5 x 12C5 (B1 for each, allow unevaluated with no extra terms)
[1] B1 Final answer must be evaluated and from multiplication (56 × 792 = 44352)
[1] M1 for realising that 4 places are accounted or that gender is no longer important
[1] A1 for 8008 (Need 16C6 = 8008)

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About this question

Topic

Permutations and combinations, O-Level Additional Mathematics (syllabus 4037). Structured question, 9 marks.

Source

O-Level Additional Mathematics, Oct/Nov 2014 Paper 1 Variant 2, question 10.

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