Question

# The number of integral solutions of the equation x+y+z+t=20, such that x≥0,y≥1,z≥2,t≥3, is

A
680
B
720
C
640
D
560

Solution

## The correct option is A 680Let X=x,Y=y−1,Z=z−2,T=t−3 then X+Y+Z+T=14 where X,Y,Z,T≥0 ∴Required number of solutions is number of non negative integral solutions  for X+Y+Z+T=14 =14+4−1C4−1=17C3=680Mathematics

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