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Question
Hi. I'd like to know how many 6 digit numbers are there of a combination of numbers 0, 2, 3, 5, 6, and 9 which can be divided to 5. None of the 6 digit numbers should be the same. But its allowed to repeat those 6 numbers in a 6 digit number. Thanks in advance. Your early response is appreciated.
Lilia

It sounds like you want to arrange the digits 0, 2, 3, 5, 6, and 9 in any order to get a six digit number that is divisible by 5.  Since there are 6 numbers, the number of ways to arrange them is 6!, but then we have to throw some out.

To start with, to be divisible by 5, they need to end in 0 or 5.  That means we can only keep
2/3 of the numbers.  Now 6! = 6*5*4*3*2*1, of which I can drop the last 1, giving 6*5*4*3*2.
It is not that difficult to multiply them out, but it is even easier to adjust the list first.

Since the string of numbers needs to be multiplied by 2/3,
note that (2/3)3 = 2, so that changes the 3 into a 2, giving 6*5*4*2*2.

Now of those numbers, 1/6 of them start with 0, and they can be dropped.

This means we only have 5/6 of the numbers left, and (5/6)6 = 5.
That makes the leading 6 into a 5, so now we have 5*5*4*2*2.

Since it is known that 5*2 is 10, and there are 2-5's at the start and 2-2's at the end,
that makes the number into 4*10*10 = 400.

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#### Scott A Wilson

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I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?

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Experience in the area; I have tutored people in the above areas of mathematics for over two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree back in 1984. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

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My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

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Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

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I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

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My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.