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?
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 = 6
Similarly, fixing the unit's digit as 4:
Number of arrangements possible = 6P2 = 6
Fixing the unit's digit as 6:
Number of arrangements possible = 6P2 = 6
∴ Number of 3-digit even numbers that can be formed = 30 + 30 + 30 = 90