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Question

The number of integral solutions of the equation x+y+z+t=20, such that x0,y1,z2,t3, is

A
680
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B
720
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C
640
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D
560
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Solution

The correct option is A 680
Let X=x,Y=y1,Z=z2,T=t3 then X+Y+Z+T=14 where X,Y,Z,T0

Required number of solutions is number of non negative integral solutions for X+Y+Z+T=14 =14+41C41=17C3=680

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