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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
a) 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 that can be set using the dials, we can calculate:
Each dial has 5 possible settings (1 through 5). Thus, the total combinations can be calculated as:
So, there are 125 different three-digit numbers that can be set for the combination lock.
Step 2
b) How many of the possible three digit numbers have three different digits?
Answer
To find the number of three-digit combinations with three different digits, we first consider the selections available:
- The first digit can be any of the 5 digits.
- The second digit can then be any of the remaining 4 digits.
- The third digit can be any of the 3 remaining digits.
Thus, the calculation can be expressed as:
Therefore, there are 60 possible three-digit numbers that have three different digits.