Find the number of positive integral solutions of `x y z=21600.`

Answer

1260

Explanation

`xyz=21600=2^(5)xx3^(3)xx5^(2)`
Number of positive integral solutions
=(Number of ways (2,2,2,2,2) can be distributed into three boxes)
`xx` (Number of ways (3,3,3) can be distributed into three boxes)
`= .^(5+3-1)C_(3) xx .^(3+3-1)C_(3-1) xx .^(2+3-1)C_(3-1)`
`= .^(7)C_(2)xx .^(5)C_(2)xx .^(4)C_(2)`
`=21xx10xx6=1260`