Correct Answer - Option 3 : 240
Given:
The given digits are 1, 4, 7, 6, 3, 5.
Concept Used:
For a number to be even, its unit digit must be an even number.
Calculation:
According to the question,
The 6-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 and 6 only i.e. there are two ways to fill the units place.
And, the remaining 5 places can be filled in 5! ways.
So,
The number of 6-digit even numbers formed using digits 1, 4, 7, 6, 3, 5 = (5! × 2)
⇒ (1 × 2 × 3 × 4 × 5) × 2
⇒ 240
∴ The number of 6-digit even numbers that can be formed from the digits 1, 4, 7, 6, 3, 5 is 240.
