2025 IGCSE Additional Mathematics October/November 0606/22 Q5

2025 IGCSE Additional Mathematics October/November 0606/22 Q5

5 marks

A 6-character password is to be formed from the following characters.

Lettersbfgkm
Numbers3579
Symbols*!@

Each character can be used at most once in any 6-character password.

  1. Find the number of 6-character passwords that can be formed if there are no further restrictions.[1]
  2. Find the number of 6-character passwords that can be formed if the password starts and ends with a symbol.[2]
  3. Find the number of 6-character passwords that can be formed if the password:[2]
    • starts with either a symbol and then a number, or a number and then a symbol and
    • ends with 2 letters.

Solution:

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Answer:(a) \(665\,280\) (b) \(30\,240\) (c) \(26\,880\)

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