1.

Find the number of positive Integral solutions of x+y+z=20 if x ne y ne z :

Answer»

144
140
146
148

SOLUTION :GIVEN `x+y+z = 20`
Required solution `PHI` Total POSITIVE Integral solution
`-` (any two are equal) `-` (`x=y=z` not possible)
`rArr .^(19)C_(2)-overset("lit (3 cases)")((x=y ne z))(z = 20-2y)`
`rArr .^(19)C_(2)-3xx(y=1, 2, .....,0)`
`rArr .^(19)C_(2)-3xx9 rArr 171 - 27 = 144`


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