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.

84

Step-by-step 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