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I know that 35 unique quadrilaterals can be formed from a heptagon by joining the vertices. I can work that out in a diagram. What I want to know is the math behind figuring this out. An equation that will work with any shape (octagon for instance), and/or how this equation is derived. Detailed explanation please.
 one year ago
 one year ago
I know that 35 unique quadrilaterals can be formed from a heptagon by joining the vertices. I can work that out in a diagram. What I want to know is the math behind figuring this out. An equation that will work with any shape (octagon for instance), and/or how this equation is derived. Detailed explanation please.
 one year ago
 one year ago

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experimentXBest ResponseYou've already chosen the best response.1
http://www.wolframalpha.com/input/?i=7+choose+4 4 vertices make quadrilaterals. Heptagon has 7 vertices. So what you are doing is choosing 4 vertices out of 7 in unique ways.
 one year ago

CliffSedgeBest ResponseYou've already chosen the best response.0
^ Combinations formula. Seems legit.
 one year ago

jagatubaBest ResponseYou've already chosen the best response.0
I do understand that, but I want to know how this can be solve with out the use of a calculator.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
choosing 'r' out of 'n' can be written as \[ \binom{n}{r} = {n! \over r! (nr)!} \]
 one year ago

jagatubaBest ResponseYou've already chosen the best response.0
Give me another example of what we are talking about that does not involve polygons.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
most common example: In a classroom you have 7 students. You have choose 5 students for basketball team. In how many different ways can you choose students.
 one year ago

jagatubaBest ResponseYou've already chosen the best response.0
Very good example: \[\left(\begin{matrix}7 \\5\end{matrix}\right)=\frac{ 7! }{ 5!(75)!}\]
 one year ago

jagatubaBest ResponseYou've already chosen the best response.0
Now is there a quicker way to figure factorials without the use of a calculator? Obviously, 15! is going to take time and be cumbersome to figure out manually. Is there a short cut?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
the topic is "Permutation and Combination" Permutation = choose something in order Combination = choose but order does not matter.  like you have two benches and 10 students. Each bench can hold 5 students. Q1. In how many ways can students sit in first bench? Q2. In how many ways can you ARRANGE student in first bench?
 one year ago

jagatubaBest ResponseYou've already chosen the best response.0
THANK YOU! That is exactly what I was looking for in the original question. Sorry if I wasn't clear.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
http://www.wolframalpha.com/input/?i=7+choose+5
 one year ago

jagatubaBest ResponseYou've already chosen the best response.0
But seriously. If you have to do some extensive factorial work without a calculator, is there a short cut to going for example; 15*14*13*12* . . . *3*2?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
lol .. .no without calculator this is horrible.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
usually in combinations, the top and bottom cancel out so that it makes thing a bit simpler. that's the only easy portion when dealing with large numbers.
 one year ago

jagatubaBest ResponseYou've already chosen the best response.0
That's what I thought. See the thing is I'm studying for my CBEST and I was told that you cannot use a calculator, but I was just taking a sample test online and there are all these factorial questions that I'm like "look, I don't want to cheat, but how am I supposed to manually figure out all of these without a calculator in the allotted amount of time?"
 one year ago

jagatubaBest ResponseYou've already chosen the best response.0
What do you mean the top and bottom cancel out?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
sorry .. numerator and denominator. when 'r' is close to 'n'. you can cancel out numerators and denominators and figure it out easily without calc.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1353182495182:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
also when 'r' is pretty close to 'n', you can do the same.
 one year ago

jagatubaBest ResponseYou've already chosen the best response.0
Oh I see, yes. Still, I'm thinking somewhere I got erroneous information. I'm think that either the CBEST does allow a calculator, OR there are not nearly that many questions that involve factorials. If anyone reading this actually has firsthand experience in taking the CBEST direct message me.
 one year ago
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