Question

From $4$ officers and $8$ jawans,
$\left(i\right)$ Let "k" be the number of ways to select $6$ from the above mentioned people .Of them there was exactly one officer.
$\left(ii\right)$ Let "m" be the number of ways to select $6$ from the above mentioned people.Of them there was at least one officer.
Find $\frac{m}{k}$ ?

Answer 1

$k{=}^4{C}_1{.}^8{C}_5=4\times 56$
$m{=}^4{C}_1{.}^8{C}_5{+}^4{C}_2{.}^8{C}_4{+}^4{C}_3{.}^8{C}_3{+}^4{C}_4{.}^8{C}_2=56\times 4\times 4$
Thus $\frac{m}{k}=4$