Question

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 while repetition of any digit is not allowed in any number

• A. 60
• B. 12
• C. 120
• D. 24

Answer 1

The correct option is B 12

Since, we required count the numbers between 3000 and 4000.
So, 3 must be at thousand place and also the number should be divisible by 5, so 5 must be at unit place.
Now we have to fill two place (ten and hundred) out of remaining digits 4, 6, 7, 8.
This can be done by ${}^4{P}_2=\frac{4!}{(4-2)!}=\frac{4\times 3\times 2\times 1}{2}=12$ ways.
Hence, the numbers that lying between 3000 and 4000 and divisible by 5 is 12.