Question

In Lotto 5-32, the lottery picks 5 numbers (without replacement) from 1 to 32. Before this drawing is done, you pick 5 numbers (without replacement) from 1 to 32. Find the probability that

(a)	none of your numbers will be among the 5 selected by the lottery.

(b)	exactly 3 of your numbers will be among the 5 selected by the lottery.

Answer 1

Number of ways to select r items from n,

nCr = n!/(r! x (n-r)!)

Number of winning numbers = 5

Total numbers = 32

Number of losing numbers = 32 - 5 = 27

a) P(none of your numbers will be among the 5 selected by the lottery) = Number of ways to select 5 numbers from non winning 27 / Number of ways to select any 5 numbers

= 27C5/32C5

= 80730/201376

= 0.400891

b) P(exactly 3 of the numbers will be among the 5 selected by the lottery) = Number of ways to select 3 winning numbers x Number of ways to select 2 losing numbers / Number of ways to select any 5 numbers

= 5C3 x 27C2 / 32C5

=(10 X 351) /201376

=0.017430