How many even numbers greater than 5000 can be formed with the
digits 1,4,5,8,9 if each digit can only be used once?
First digit 5, 8 or 9
last digit: 4 or 8
Case1: 1st digit 8, last digit 4
3 X 2 = 6
Case 2: 1st digit 9, last digit 4
3 X 2 = 6
Case 3: 1st digit 9, last digit 8
3 X 2 = 6
Case 4: 1st digit 5 , last digit 4 or
8 3 X 2 X 2 =
12
The answer given is 78
The answer given is incorrect.
If last digit is 4, number of possibilities = 3 X 3 X 2 = 18
If last digit is 8, number of possibilities = 2 X 3 X 2 = 12
Total = 30 ways.
A simple way to prove that the answer is wrong:
Total ways with no restriction except non-repetition = 5 X 4 X 3
X 2 = 120
Total numbers less than 5000 = 2 X 4 X 3 X 2 = 48
Numbers more than 5000 ( Both odd and even ) = 120 - 48 = 72,
which is a contradiction to the answer given.
