Duration: 5:40

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There are math xmlns=http://www.w3.org/1998/Math/MathMLmn5/mn/math students in class math xmlns=http://www.w3.org/1998/Math/MathMLmn10/mnmo,/momo /momn6/mn/math students in class math xmlns=http://www.w3.org/1998/Math/MathMLmn11/mn/math and math xmlns=http://www.w3.org/1998/Math/MathMLmn8/mn/math students in class math xmlns=http://www.w3.org/1998/Math/MathMLmn12/mn/math. If the number of ways, in which math xmlns=http://www.w3.org/1998/Math/MathMLmn10/mn/math students can be selected from them so as to include at least math xmlns=http://www.w3.org/1998/Math/MathMLmn2/mn/math students from each class and at most math xmlns=http://www.w3.org/1998/Math/MathMLmn5/mn/math students from the total math xmlns=http://www.w3.org/1998/Math/MathMLmn11/mn/math students of class math xmlns=http://www.w3.org/1998/Math/MathMLmn10/mn/math and math xmlns=http://www.w3.org/1998/Math/MathMLmn11/mn/math is \( 100 \mathrm{k} \), then \( k \) is equal to
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