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Find the number of 6-digit even numbers that can be formed from the digits 1, 4, 7, 6, 3, 5 when the repetition of digits is not allowed.

Find the number of 6-digit even numbers that can be formed from the digits 1, 4, 7, 6, 3, 5 when the repetition of digits is not allowed. Correct Answer 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.

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