Question

Here are three digits: 1, 9,8

Write down a number between 600 and 900 that uses each of these digits once.

Answer 1

Explanation:

Numbers begin with ‘8’:

Integers from 800 to 899; that is 100 numbers.

Numbers end with ‘8’ from 600 to 900:

Options for hundred's place = 3 (digits ‘6’, ‘7’ and ‘8’).

Options for ten's place = 10 (all ten digits)

Options for unit's place = 1 (only ‘8’)

So, (3 * 10 * 1) = 30 numbers.

Now, among these (100 + 30) = 130 numbers; there are some which start and end with ‘8’; we need to eliminate them to avoid ‘double counting’ of these numbers. How many are they?

Numbers start and end with ‘8’:

Option for hundred's place = 1 (Only ‘8’)

Options for ten's place = 10 (all ten digits)

Option for unit's place = 1 (only ‘8’)

So, (1 * 10 * 1) = 10 numbers.

Therefore, there are (130 - 10) = 120 numbers from 600 to 900 which either start with ‘8’ or end with ‘8’.