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<H1 CLASS="Heading-1"> <font color="#0000A0">The factorial and combin Functions</font></H1>
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<H2 CLASS="program0"> from visual import *</H2>
<H2 CLASS="program0">from visual.factorial import *</H2>
<H2 CLASS="program0">factorial(N) = N! </H2>
<h2 class="program0">combin(a,b) = a!/(b!*(a-b)!)</h2>
<p class="Normal"> </p>
<P CLASS="Normal"><em>Note: To avoid confusion between the module named "factorial"
and the function named "factorial", import the factorial module
<strong>after</strong> importing the visual module itself.</em></P>
<P CLASS="Normal">A major use of these functions is in calculating the number
of ways of arranging a group of objects. For example, if there are 5 numbered
balls in a sack, there are <span class="attribute">factorial(5)</span> =
5! = 5*4*3*2*1 = 120 ways of taking them sequentially out of the sack (5
possibilities for the first ball, 4 for the next, and so on). </P>
<P CLASS="Normal">If on the other hand the 5 balls are not numbered, but 2
are green and 3 are red, of the 120 ways of picking the balls there are
2! indistinguishable ways of arranging the green balls and 3! ways of arranging
the red balls, so the number of different arrangements of the balls is <span class="attribute">combin(5,2)</span>
= 5!/(3!*2!) = 10.</P>
<P CLASS="Normal">Logically, the combin function is just a combination of
factorial functions. However, cancellations in the numerator and denominator
make it possible to evaluate the combin function for values of its arguments
that would overflow the factorial function, due to the limited size of floating-point
numbers. For example, <span class="attribute">combin(5,2)</span> = 5!/(3!*2!)
= (5*4)/2 = 10, and we didn't have to evaluate 5! fully.</P>
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