O-LevelAdditional MathematicsPermutations and combinations4037/22 · Oct/Nov 2018 · Q66 Marks
A 5-character code is to be formed from the 13 characters shown below. Each character may be used once only in any code. Letters: A, B, C, D, E, F Numbers: 1, 2, 3, 4, 5, 6, 7 Find the number of different codes in which no two letters follow each other and no two numbers follow each other.
- (a)A 5-character code is to be formed from the 13 characters shown below. Each character may be used once only in any code. Letters: A, B, C, D, E, F Numbers: 1, 2, 3, 4, 5, 6, 7 Find the number of different codes in which no two letters follow each other and no two numbers follow each other.[3]
- (b)A netball team of 7 players is to be chosen from 10 girls. 3 of these 10 girls are sisters. Find the number of different ways the team can be chosen if the team does not contain all 3 sisters.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.
- [B1] Number first = 7×6×5×6×5 or ⁷P₅ × ⁶P₅ or 6300
- [B1] Letter first = 6×5×4×7×6 or ⁶P₅ × ⁷P₅ or 5040
- [B1] 6300+5040 = 11 340
- [B1] Total no of ways = ¹⁰C₇ = 120
- [B1] With 3 sisters = ⁷C₄ = 35
- [B1] Without 3 sisters = 120-35=85
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