SOLUTION: How many numbers between 4000 an 5000 can be formed with the digit 2,3,4,5,6,7? How many of these numbers are divisible by 5?

Question 483262: How many numbers between 4000 an 5000 can be formed with the digit 2,3,4,5,6,7? How many of these numbers are divisible by 5?

Found 2 solutions by josmiceli, mathstutor494:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The first digit has to be since
is the smallest number I
can make with as the MSD
There are ways to make
numbers starting with ( allowing repetitions )
is the smallest
Divisible by means the LSD
is a .
The number will always look like 4**5
so there are numbers divisible
by
Answer by mathstutor494(120) (Show Source): You can put this solution on YOUR website!
Numbers between 4000 an 5000 would start with 4 and will have 4 digits.
So the first position will be filled by 4 and the number would look like
4 _ _ _
Then the remaining 3 digits will be formed from remaining 5 digit 2,3,5,6,7 in 5P3 ways (no repeatitions).
Numbers formed = 1. 5P3
= 5!/(5-3)!
= 5*4*3
= 60
In order for these numbers to be divisible by 5, the number would be
4 - - 5
And the number would be formed by filling up 2nd and 3rd digit from the remaining 4 digits 2,3,6,7 in 4P2 ways i.e 4*3 = 12

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