How many 4-digit numbers(without repetition) can be formed from the di

1.	How many 4-digit numbers(without repetition) can be formed from the digits 4, 5, 6, 7, 8, 9 which are divisible by 2?1. 2802. 1803. 3404. 4005. None of the above/More than one of the above.
Answer» Correct Answer - Option 2 : 180 Given: The given digits are4, 5, 6, 7, 8, 9. Concept Used: For a number to be even, its unit digit must be an even number. Calculation: According to the question, The 4-digit numbers to be formed must be even numbers. For that to happen, the unit digit of the numbers must be even. So, the units place can be filled by 4, 6, and 8 only i.e. there are three ways to fill the units place. After filling units place, there are 5 digits left. So, the 4thplacecan be filled in 5ways. Similarly, the 3rd place and 2nd place can be filled in 4 and 3 ways respectively. The number of 4-digit even numbers formed using digits4, 5, 6, 7, 8, 9 = (5× 4× 3) × 3 ⇒ 180 ∴ The number of 4-digit even numbers that can be formed from the digits 4, 5, 6, 7, 8, 9 is 180.

How many 4-digit numbers(without repetition) can be formed from the digits 4, 5, 6, 7, 8, 9 which are divisible by 2?1. 2802. 1803. 3404. 4005. None of the above/More than one of the above.

Answer» Correct Answer - Option 2 : 180

Given:

The given digits are4, 5, 6, 7, 8, 9.

Concept Used:

For a number to be even, its unit digit must be an even number.

Calculation:

According to the question,

The 4-digit numbers to be formed must be even numbers. For that to happen, the unit digit of the numbers must be even.

So, the units place can be filled by 4, 6, and 8 only i.e. there are three ways to fill the units place.

After filling units place, there are 5 digits left.

So, the 4thplacecan be filled in 5ways.

Similarly, the 3rd place and 2nd place can be filled in 4 and 3 ways respectively.

The number of 4-digit even numbers formed using digits4, 5, 6, 7, 8, 9 = (5× 4× 3) × 3

⇒ 180

∴ The number of 4-digit even numbers that can be formed from the digits 4, 5, 6, 7, 8, 9 is 180.