Alocal lottery is conducted weekly by choosing five chips atrandom and without replacement from a population of 40 chips, numbered 1 through 40; order does not matter. the winning numbersare announced on five successive commercials during the mondaynight broadcast of a televised movie. suppose the first threewinning numbers mathc three of yours. what are your chances at thatpoint of winning the lottery?

0.002

Step-by-step explanation:

The order of choosing the 5 chips without replacement from a population of 40 chips does not matter, so I decide to choose 3 chips first which match the winning numbers

Number of chips left = 40 - 3 = 37, number of chips left to be chosen = 5 - 3 = 2

The number of ways to choose the remaining 2 chips from the 37 chips left can be done by the combination method

Number of ways = n combination r = n!/(n - r)!r!

n = 37, r = 2

Number of ways = 37!/(37-2)!2! = 37!/35!2! = 37×36×35!/35!×2 = 37×36/2 = 37×18 = 666

My chances of winning = 1/666 = 0.002

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