How many 5 digit numbers can be formed with 0,1,2,3,5, which are divisible by 5?

Question

i have a ton of math homework to do and this is one of those questions which i gave up on. help me..................

Answer 1

Thirty-nine (39):
10235, 10325, 12035, 12305, 12350, 12530, 13025, 13205, 13250, 13520, 15230, 15320, 20135, 20315, 21305, 21350, 21530, 23105, 23150, 23510, 25130, 25310, 30125, 30215, 31205, 31250, 31520, 32015, 32105, 32150, 32510, 35120, 35210, 51230, 51320, 52130, 52310, 53120, 53210.

Nina listed 13250 and 13520 twice, and missed 13025 and 13205, but was right that there are 12 five-digit numbers starting with 1 including 0,1,2,3 and 5. But her theory that 42 numbers results does not play out. Instead it comes out to 39.

She's right that here are less number combinations starting with 5 because 5 is one of the numbers that can be a valid end number that is divisible by 5, so only 6 result. But it turns out there are only 10 numbers beginning with 2 and 11 beginning with 3, not 12 in either case. This is because there are four 25 and 35 combinations with the 10000 series, but only two combined through the 20000 and 30000 series and only two combined 15 combinations to make up for it.

As for Gary Popkin's calculations, although he makes the premise that he's not limiting his combinations to true 5-digit numbers (i.e., that cannot begin with zero), his calculations don't limit the combinations to 5-digit numbers. His prediction of 1000 combinations, therefore, is way off.

Answer 2

theres 42. All the numbers have to end in 5 or 0 for it to be divisible by 5. first try to find all the patters that can begin with 1.
12350
12530
15320
15230
13250
13520
12305
12035
10235
10325
13250
13520

Ok there r 12 patters if the number begging in 1. Since number can also begin with 2 and 3 u multiply 12 by 3. You get 36. But numbers can begin wit 5 too so instead of adding 12 to 36 u add half of 12 which is 6, to 36 and u get 42. you dont add 12 because that would mean that the numbers beginning with five can also end in 5 and that cant be true cuz u only have one 5 digit. So the solution again, theres 42 ways.


Please mark as the best answer. Thank You. =]

Answer 3

Let's assume these have to be real 5-digit numbers, not starting with zero.

For a number to be divisable by 5, it must end in 5 or 0.

Let's see how many 5-digit numbers end in 0:

The first digit can be 1, 2, 3, or 5.
The second digit can be 1, 2, 3, 5, or 0.
The third digit can be 1, 2, 3, 5, or 0.
The fourth digit can be 1, 2, 3, 5, or 0.

Right?

So there are 4 * 5 * 5 * 5 numbers that end in 0. That's 500.

How many numbers end in 5? The same reasoning applies, and we get another 500, for a total of 1,000.

Answer 4

1235
12350
12305
12035
12530 14 ways (i think)
1325
13250
13205
13520
13025
15230
15320
10235
10325

Answer 5

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