Find the value of `r,` if
(i) `.^(11)P_(r)=990`
(ii) `.^(8)P_(5)+5*^(8)P_(4)=^(9)P_(r)`

Explanation

(i) `because.^(11)P_(r)=990=11xx10xx9=.^(11)P_(3)`
`thereforer=3`
(ii) `because .^(8)P_(5)+5*.^(8)P_(4)=.^(9)P_(r)`
`implies.^(8)P_(4)((.^(8)P_(5))/(.^(8)P_(4))+5)=.^(9)P_(r)`
`implies.^(8)P_(4)(8-5+1+5)=.^(9)P_(r)` [ from note (v)]
`implies9*.^(8)P_(4)=.^(9)P_(r)`
`implies.^(9)P_(5)=.^(9)P_(r)` [from note (iii)]
`thereforer=5`