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Question
Find number of non negative integral solution of equation x+y+z=−12.
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Solution
According to question.....
x+y+z=−12∣∣
∣
∣∣x=x′−1y=y′−1z=z′−1x′−1+y′−1+z′−1=−12x′+y′+z′=−12+3=−9No.ofways⇒9+3−1C3−1∣∣∣x1+x2+x3...xm=nn+m−1Cm−1⇒11C2=11×102=55sothat,thenon negative integral solutionis55.
x+y+z=−12∣∣
∣
∣∣x=x′−1y=y′−1z=z′−1x′−1+y′−1+z′−1=−12x′+y′+z′=−12+3=−9No.ofways⇒9+3−1C3−1∣∣∣x1+x2+x3...xm=nn+m−1Cm−1⇒11C2=11×102=55sothat,thenon negative integral solutionis55.
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