Answer to Question #201171 in Statistics and Probability for Zaki

Question

How many 3 digits numbers are possible using the digits 0, 1, 2, 3, 4 each digit using only once. 

⦁ Numbers are odd.

⦁ Numbers are even.

Answer 1

Solution:

We have three places to fill (_ _ _) in a number of 3-digits. We can use 0, 1, 2, 3, 4 only once.

0 cannot come at hundred's place.

(1) Numbers are odd:

One's place can only contain 1 or 3.

So the number of ways one's place can be filled = 2

Then hundred's place can only contain 2 or 4 and one digit remaining out of 1 or 3

The number of ways hundred's place can be filled = 3

Then the number of ways ten's place can be filled = 2

Total numbers formed = 2 x 2 x 3 = 12

(2) Numbers are even:

One's place can only contain 0, 2 or 4.

So the number of ways one's place can be filled = 3

The number of ways hundred's place can be filled = 3

Then the number of ways ten's place can be filled = 2

Total numbers formed = 3 x 3 x 2 = 18