The number of solutions of a+b+c+d+e+f = 2006 is 9.12 * 10^16
<h3>How to determine the number of solutions?</h3>
The equation is given as:
a+b+c+d+e+f = 2006
In the above equation, we have:
Result = 2006
Variables = 6
This means that
n = 2006
r = 6
The number of solutions is then calculated as:
(n + r - 1)Cr
This gives
(2006 + 6 - 1)C6
Evaluate the sum and difference
2011C6
Apply the combination formula:
2011C6 = 2011!/((2011-6)! * 6!)
Evaluate the difference
2011C6 = 2011!/(2005! * 6!)
Expand the expression
2011C6 = 2011 * 2010 * 2009 * 2008 * 2007 * 2006 * 2005!/(2005! * 6!)
Cancel out the common factors
2011C6 = 2011 * 2010 * 2009 * 2008 * 2007 * 2006/6!
Expand the denominator
2011C6 = 2011 * 2010 * 2009 * 2008 * 2007 * 2006/720
Evaluate the quotient
2011C6 = 9.12 * 10^16
Hence, the number of solutions of a+b+c+d+e+f = 2006 is 9.12 * 10^16
Read more about combinations at:
brainly.com/question/11732255
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