2025 IGCSE Additional Mathematics May/June 0606/22 Q5

2025 IGCSE Additional Mathematics May/June 0606/22 Q5

8 marks
  1. A 4-digit number is to be formed using the digits 0, 2, 4, 5, 6 and 8.
    The 4-digit number must not start with 0.
    Any digit may be used at most once in the 4-digit number.
    1. Find how many 4-digit numbers can be formed.[1]
    2. Find how many even 4-digit numbers can be formed.[2]
    3. Find how many 4-digit numbers that are divisible by 5 can be formed.[2]
  2. Solve the equation \((n+1)\times{}^{n+1}\mathrm C_{12}=33(n-10)\times{}^n\mathrm C_{10}\).[3]

Solution:

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Answer:(a)(i) \(300\) (ii) \(252\) (iii) \(108\) (b) \(n=65\)

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