If `\ ^(28)C_(2r):\ ^(24)C_(2r-4)=225 : 11` ,find r

Explanation

We have, `\ ^{28} C_{2 r}:\ ^{24} C_{2 r-4}=225: 11`

`Rightarrow frac{\ ^{28} C_{2 r}}{\ ^{24} C_{2 r-4}}=frac{225}{11} `

`Rightarrow frac{28 !}{2 r !(28-2 r) !} times frac{(2 r-4) !(28-2 r) !}{24 !}=frac{225}{11} `

`Rightarrow frac{28 times 27 times 26 times 25}{2 r(2 r-1)(2 r-2)(2 r-3)}=frac{225}{11} `

`Rightarrow 2 r(2 r-1)(2 r-2)(2 r-3)=frac{28 times 27 times 26 times 25 times 11}{225} `

`Rightarrow 2 r(2 r-1)(2 r-2)(2 r-3)=28 times 3 times 26 times 11 `

`Rightarrow 2 r(2 r-1)(2 r-2)(2 r-3)=4 times 7 times 3 times 13 times 2 times 11 `

`Rightarrow 2 r(2 r-1)(2 r-2)(2 r-3)=(2 times 7) times 13 times(3 times 4) times 11 `

...