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  4. How many numbers can be made with the digits 3,4,5, 6,7,8 lying between 3000 and 4000 which are divisible by 5 whereas repetition of any digit is not allowed in any number?

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Q. How many numbers can be made with the digits $3,4,5$, $6,7,8$ lying between $3000$ and $4000$ which are divisible by $5$ whereas repetition of any digit is not allowed in any number?

Permutations and Combinations

Solution:

$3$ must be at $1000\, th$ place because the number should be divisible by $5,$ or $5$ must be at unit place.
Now, we have to fill two places ($10$ and $100$), that is, ${ }^{4} P_{2}=12$