O-LevelAdditional MathematicsPermutations and combinations4037/12 · Oct/Nov 2013 · Q77 Marks

Find how many different 4-digit numbers can be formed from the digits 1, 3, 5, 6, 8 and 9 if each digit may be used only once.

(a)(i)Find how many different 4-digit numbers can be formed from the digits 1, 3, 5, 6, 8 and 9 if each digit may be used only once.[1]
(a)(ii)Find how many of these 4-digit numbers are even.[1]
(b)A team of 6 people is to be selected from 8 men and 4 women. Find the number of different teams that can be selected if
(b)(i)there are no restrictions,[1]
(b)(ii)the team contains all 4 women,[1]
(b)(iii)the team contains at least 4 men.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2013). The mark or mark type is shown in brackets.

[B1] (a) (i) 360
[B1] (a) (ii) 120
[B1] (b) (i) 924
[B1] (b) (ii) 28
[M1] (b) (iii) for 3 terms, at least 2 of which must be correct in terms of C notation or evaluated. (e.g. 924 -(⁸C₃ × ⁴C₃)-(⁸C₂ × ⁴C₄))
[A1] for any pair (must be evaluated)
[A1] for final answer (672)
Or:
[M1] for 3 terms, at least 2 of which must be correct in terms of C notation or evaluated. (e.g. ⁸C₄ × ⁴C₂ + ⁸C₅ × ⁴C₁ + ⁸C₆)
[A1] for any pair (must be evaluated)
[A1] for final answer (672)

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