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Question
How many five-digit numbers formed using the digit 0, 1, 2, 3, 4, 5 are divisible by 5 if digits are not repeated?
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Solution
For a number to be divisible by 5,
Unit’s place digit should be 0 or 5.
Case I: when unit’s place is 0
Unit’s place digit can be selected in 1 way.
10’s place digit can be selected in 5 ways.
100’s place digit can be selected in 4 ways.
1000’s place digit can be selected in 3 ways.
10000’s place digit can be selected in 2 ways.
∴ total number of numbers = 1 × 5 × 4 × 3 × 2 = 120
Case II: when unit’s place is 5
Unit’s place digit can be selected in 1 way
10000’s place should be a non-zero number
∴ It can be selected in 4 ways
1000’s place digit can be selected in 4 ways.
100’s place digit can be selected in 3 ways.
10’s place digit can be selected in 2 ways.
∴ total number of numbers = 1 × 4 × 4 × 3 × 2 = 96
∴ Required number = 120 + 96 = 216
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