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Question
How many 3-digit even number can be made using the digits 1, 2, 3, 4, 5, 6, 7, if no digits is repeated?
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Solution
In order to find the number of even digits, we fix the unit's digit as an even digit.
Fixing the unit's digit as 2:
Number of arrangements possible = 6P2 = `6xx5=30`
Similarly, fixing the unit's digit as 4:
Number of arrangements possible = 6P2 = `6xx5=30`
Fixing the unit's digit as 6:
Number of arrangements possible = 6P2 =`6xx5=30`
∴ Number of 3-digit even numbers that can be formed = 30 + 30 + 30 = 90
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