Question

How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 5, 6, 7, if no digits is repeated?

Answer 1

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
= $6_{P_2}=6\times 5=30$
Similarly, fixing the units digit as 4 :
Number of arrangements possible
= $6_{P_2}=6\times 5=30$
Fixing the unit's digit as 6:
Number of arrangements possible
= $6_{P_2}=6\times 5=30$
\therefore Number of 3 -digit even numbers that can be formed = 30+30+30 = 90