Sum

Find the number of 6-digit numbers using the digits 3, 4, 5, 6, 7, 8 without repetition. How many of these numbers are divisible by 5?

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#### Solution

We have to form 6 digit numbers using the digits 3, 4, 5, 6, 7, 8 without repetition.

Total number of ways of arranging 6 digits in six places = ^{6}P_{6} = 6!

= 6 × 5 × 4 × 3 × 2 × 1 = 720 ways

Here, the number is divisible by 5. So it will have the digit 5 in the unit’s place.

Hence, the unit’s place can be filled in 1 way.

The other five places can be filled in by the remaining 5 digits

(Since repetition is not allowed) in ^{5}P_{5} = 5! Ways.

Total number of ways in which numbers divisible by 5 can be formed = 1 × 5! = 120

Concept: Concept of Permutations - Permutations When Repetitions Are Allowed

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