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How many solutions does $a + b + c + d = 20$ have if each of a, $b, c, d$ is a whole number at least 3?

Competition practicePermutations & Combinations

A165
B1771
C120
D330

Step-by-Step Solution

Give 3 to each variable first (12 used), leaving 8 to share freely among 4:

^{8 + 3} C_{3} =^{11} C_{3} = 165. (1771 =^{23} C_{3}

drops the lower limit.)

Answer: A) 165

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