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Find the number of non-negative integral...

Find the number of non-negative integral solutions of `x+y+z+wlt=20.`

Text Solution

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We have inequality, `x+y+z+w le 20`
This is equivalent to equation
x+y+z+w+t=20, where `t ge 0`
Clearly number of non-negative integral solutions to (1) and (2) are same.
So, number of solutions `= .^(20+5-1)C_(5-1)= .^(24)C_(4)`
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