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Find the number of solutions of `x + y + z + w = 20` under the following conditions: 1) x,y,z,w are whole number 2) x,y,z,w are natural number

Text Solution

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Since, `x+y+z+w=20`
here, `x ge 0, y ge 0, z ge 0, w ge0`
The number of sols of the given equation in this case is same as the number of ways of distributing 20 things among 4 different groups.
Hence, total number of sols`=.^(20+4-1)C_(4-1)`
`=^(23)C_(3)=(23*22*21)/(1*2*3)=1771`.
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