Question

Find the number of 3-digit numbers formed using the digits 1 to 9, without repetition, such the numbers either have all digits less than 5 or all digits greater than 4.

Answer 1

84

Explanation:

Given,

The possible digits are 9 ( i.e. 1, 2, 3, 4, 5, 6, 7, 8, 9 )

Digits less than 5 = 4 ( i.e. 1, 2, 3, 4 )

Digits greater than 4 = 5 ( i.e. 5, 6, 7, 8, 9 )

Here, we need to make 3 digit number from these digits without repeating,

If digits are less than 5,

Then the possible ways = 4 × 3 × 2

= 24

If digits are greater than 4,

Then the possible ways = 5 × 4 × 3

= 60

Hence, the total ways of choosing three digits number without repeating if all digits are less than 5 or all digits are greater than 4

= 24 + 60

= 84