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Question

The number of integral solutions for the equation x+y+z+t=20, where x,y,z,t are all 1, is

A
20C4
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B
23C3
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C
27C4
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D
27C3
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Solution

The correct option is D 27C3
Given x+y+z+t=20
x1,y1,z1 and t1
Put x+1=x1,y+1=x2,z+1=x3,t+1=x4
(where x1,x2,x3,x40)
Hence given equation becomes x1+x2+x3+x4=24
Number of non-negative integral solutions =(24+41)C41=27C3

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