A-LevelMathematicsProbability and statistics9709/53 · Oct/Nov 2021 · Q58 Marks
A security code consists of 2 letters followed by a 4-digit number. The letters are chosen from {A, B, C, D, E} and the digits are chosen from {1, 2, 3, 4, 5, 6, 7}. No letter or digit may appear more than once. An example of a code is BE3216.
- (a)How many different codes can be formed?[2]
- (b)Find the number of different codes that include the letter A or the digit 5 or both.[3]
- (c)A security code is formed at random. Find the probability that the code is DE followed by a number between 4500 and 5000.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.
- [M1] ⁵P₂ × ⁷P₄ or 5 × 4 × 7 × 6 × 5 × 4
- [A1]
- [M1] ⁴P₂ × ⁶P₄ or ⁴C₂ × ⁶C₄ seen, accept unsimplified.
- [M1] Their 5(a) (or correct) – their (No A or 5) value.
- [A1]
- [M1] 3 × ⁵Pn, n = 2, 3. Condone 3 × ⁵C₂, no + or –.
- [M1] Probability = their 60 / their 16 800
- [A1]
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