Question Number 193292 by byaw last updated on 09/Jun/23
$$ \\ $$(a) A man P has 5 red, 3 blue and 2 white buses. Another man Q has 3 red, 2 blue and 4 white buses. A bus owned by P is involved in an accident with a bus belonging to Q. Calculate the probability that the two buses are not of the same color.
(b) A man travels from Nigeria to Ghana by air and from Ghana to Liberia by ship. He returns by the same means. He has 6 airlines and 4 shipping lines to choose from. In how many ways can he make his journey without using the same airline or shipping line twice?
Answered by MM42 last updated on 09/Jun/23
$$\left.{a}\right)\:\:{if}\:\:{A}={rr}\:\cup{bb}\cup{ww}\:\:{the}\:{set}\:{is}\:{the}\:{same}\:{color}\:{then} \\ $$$${thr}\:{sey}?{of}\:{non}−{uniformity}\:{in}\:{the}\:{face} \\ $$$${A}'={rb}\cup{br}\cup{rw}\cup{wb}\cup{bw}\cup{wb} \\ $$$$\Rightarrow{p}\left({A}\right)=\frac{\mathrm{5}}{\mathrm{10}}×\frac{\mathrm{3}}{\mathrm{9}}+\frac{\mathrm{4}}{\mathrm{10}}×\frac{\mathrm{2}}{\mathrm{9}}+\frac{\mathrm{2}}{\mathrm{10}}×\frac{\mathrm{4}}{\mathrm{9}}=\frac{\mathrm{29}}{\mathrm{90}} \\ $$$$\Rightarrow{p}\left({A}'\right)=\mathrm{1}−\frac{\mathrm{29}}{\mathrm{90}}=\frac{\mathrm{61}}{\mathrm{90}} \\ $$$$\left.{b}\right){n}\overset{\mathrm{6}} {\rightarrow}{g}\overset{\mathrm{4}} {\rightarrow}{l}\overset{\mathrm{3}} {\rightarrow}{g}\overset{\mathrm{5}} {\rightarrow}{n}\Rightarrow{ans}=\mathrm{6}×\mathrm{4}×\mathrm{3}×\mathrm{5}=\mathrm{360}\: \\ $$