Question

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 514 is one way the dials can be set as shown in the diagram.

a) Work out the number of different three digit numbers that can be set for the combination lock.

b) How many of the possible three digit numbers have three different digits? ​

Answer 1

a) 125 different numbers

b) 60 numbers with different digits

Explanation:

You want to know the number of different combinations you can have with three dials, each having numbers 1–5, and you want to know the number of combinations with three different digits.

a) Combinations

Any of the three dials may be set to any of the five digits, so there are ...

5 × 5 × 5 = 125

possible three digit combinations.

The number of different 3-digit numbers is 125.

b) Different digits

If the digits are to be different, there can be 5 different first digits, 4 different second digits, and 3 different 3rd digits, for a total of ...

5 × 4 × 3 = 60

possible combinations with different digits.

The number of 3-digit numbers with different digits is 60.

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