Question

Find an article or advertisement about lottery in which choosing a winner involves combinations where nCr is read as the number of combinations of n items taken r at a time. Calculate the probability of winning that particular game. Does your calculations agree with the advertised probability? Explain.

Answer 1

As advertised :

P(winning) = 1/10 = 0.1 {1 out of 10 people win}

Actual Probability of winning :

P(winning) = 1 / nCr = 1 / 5C2 = 1 / (5! / ((2!)*(5-2)!)) = 1/10 = 0.1

as we can see P(winning)advertised = P(winning)actual

Therefore our calculations agree with the advertised probability

P.S. (please upvote if you find the answer satisfactory)