Math: counting: how many ways can four whole numbers sum to 10?
Tutoring math, you might be asked counting problems. The tutor brings up one.
How many solutions can be found to x1 + x2 + x3 + x4 = 10, where x1, x2, x3, and x4 are all whole numbers?
Imagine three pipes |||, and ten asterisks **********. Then 5, for example, appears as *****. The pipes separate the values of x1, x2, x3, and x4. Therefore, the solution x1=3, x2 =0,x3=5, x4=2 shows as
***||*****|**
By the guidelines above, any solution to x1 + x2 + x3 + x4 = 10 can be shown as a sequence of 13 characters: three pipes and ten asterisks. The variability is which three positions the pipes occupy. 13C3 is how many ways the pipes can be distributed. Therefore, there are 13C3 solutions to x1 + x2 + x3 + x4 = 10, where x1, x2, x3, and x4 are all whole numbers.
Source:
Ross, Sheldon. A First Course in Probability. New York: Macmillan Publishing Company, 1988.
Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.
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