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Advanced Math/8 Planets in 12 Signs

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Expert: - 4/11/2010


Question
Hi Scott,

Can you explain with proper formula that how to count maximum possibilities of 8 different planets' situation in 12 different signs?

I know that the "formula" for the number of distinct configurations of P planets in S signs is  S^P where ^ means "raised to the power of".
So, for 8 planets and 12 signs, the number of possible configurations is:
12^8, or 12*12*12*12*12*12*12*12, or 429,981,696
But
Mercury and Venus is always with the Sun. Mercury can be far maximum 1 sign before or after the Sun. Venus can be far maximum 2 Sign before or after the Sun.
Eg.
If the Sun is in sign 6,
Moon can be in Sign 1, Sign 2, Sign 3, Sign 4, Sign 5, Sign 6, Sign 7, Sign 8, Sign 9, Sign 10, Sign 11 or in Sign 12.
Same way, Mars, Jupiter, Saturn and Node can be far upto 12 signs from the Sun.

But in case of Mercury and Venus,
If sun is in sign 6,
Mercury and Venus cannot be in certain signs.
Mercury can be only in Sign 5, Sign 6 or in Sign 7. (Can be one sign away from Sun)
Venus can be only in Sign 4, Sign 5, Sign 6, Sign 7 or Sign 8. (Can be Two signs away from the Sun)

So we have to reduce some configurations among 429,981,696. What to do?
Can we use nCr or nPr  to find out the number of configurations that we have to reduce from 429,981,696 or this can be done with the help of the formula S^P or any other way?

I hope you will give me the final-last Number of possible ways of planetary positions in twelve signs with Explanation.
Thank You

Answer
From what I understand of what you said ...

There are 12 different signs.
There are 3 signf for mercury.
There are 5 signs for venus.
There are 12 signs for the moon, mars, jupiter, saturn, and the node, for a total of 12.

Thus, multiplying these out gives 3*5*12^5.
This would give 3*5*12*12*12*12*12.  That would be 3,732,480.

Is that what is being looked for?

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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 even tell you it takes me over 2,000 steps to go a mile, but is that relevant?

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Experience in the area; I have tutored people in the above areas of mathematics for almost two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree almost 25 years ago. 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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