# How Many 3-digit Even Number Can Be Made Using the Digits 1, 2, 3, 4, 5, 6, 7, If No Digits is Repeated? - Mathematics

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  = 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

Concept: Factorial N (N!) Permutations and Combinations
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 16 Permutations
Exercise 16.3 | Q 30 | Page 29