How many solutions does the equation A+B+C=5 have if A, B, and C are non negative integers?

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How many solutions does the equation A+B+C=5 have if A, B, and C are non negative integers?

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Answer 1 · 2015-12-15T15:49:12

#21#

Explanation:

If #A=0# there are #6# possible values for #B: [0,5]#
If #A=1# there are #5# possible values for #B: [0,4]#
If #A=2# there are #4# possible values for #B: [0,3]#
and so on.

Once choices have been made for #A# and #B# there is only ever #1# choice for #C#

Therefore the number of solutions is
#6+5+4+3+2+1 = 21#

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How many solutions does the equation A+B+C=5 have if A, B, and C are non negative integers?

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