Problem
COM-B2-M03-P003 Nonnegative Solutions
#3
★★☆☆☆ Level 2 of 5
How many nonnegative integer solutions does \(x_1+x_2+x_3=10\) have?
com_3.md (method inspiration)
Use \(10\) stars and \(2\) bars.
A solution corresponds to a string of \(10\) stars and \(2\) bars: the numbers of stars in the three gaps are \(x_1,x_2,x_3\). Conversely, every such string gives a solution. There are \(\binom{12}{2}=66\) strings.
Watch that zeros are allowed.