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There are three dials on a combination lock - Edexcel - GCSE Maths - Question 17 - 2019 - Paper 1
Question 17
There are three dials on a combination lock. Each dial can be set to one of the numbers 1, 2, 3, 4, 5. The three digit number 553 is one way the dials can be set. (... show full transcript
Worked Solution & Example Answer:There are three dials on a combination lock - Edexcel - GCSE Maths - Question 17 - 2019 - Paper 1
Step 1
Work out the number of different three digit numbers that can be set for the combination lock.
Answer
To determine the total number of different three-digit combinations possible with three dials, where each dial can be set to one of five digits (1 through 5), we can use the formula for combinations with repetition.
Since each dial operates independently, we calculate:
Thus, there are 125 different three-digit numbers that can be set for the combination lock.
Step 2
How many of the possible three digit numbers have three different digits?
Answer
To find the number of three-digit combinations that contain three different digits, we first determine the total combinations possible with 3 different digits. We select the first digit, second digit, and third digit while ensuring they are distinct:
- First digit: There are 5 options (1, 2, 3, 4, 5).
- Second digit: There are 4 remaining options after selecting the first digit.
- Third digit: There are 3 remaining options after selecting the first two digits.
Thus, the total number of different three-digit combinations with distinct digits is:
Therefore, 60 of the possible three-digit numbers have three different digits.