The number of ways to pick 6 different numbers from 1 to 40 in a state lottery is 3,803,830. assuming order is unimportant, what is the probability of picking exactly 4 of the 6 numbers correctly?

To play, we first choose 6 numbers out of 40. (Odds of matching all 6 numbers is 1 in 3,803,830.)

Then we have to match 4 of the 6 winning numbers. In how many ways can 4 numbers be chosen from the winning 6? We use the formula n! / [r! * (n-r)!]

6! / [4! * 2!] = (6 * 5) / 2 which equals 15

Since we can ONLY match 4 numbers, we must determine how many ways we can choose 2 numbers from the remaining 34 LOSING numbers.

34! / [ 2! * (34 -2)!] = (34 * 33) / 2 which equals 561.

Next we multiply 15 * 561 which equals the number of ways we can choose 4 of the 6 WINNING numbers plus 2 of the 34 LOSING numbers.

15 * 561 = 8,415

FINALLY, we divide that number by 3,803,830 which gives us the probability of choosing EXACTLY four of the six winning numbers from a set of 40.

8,415 / 3,803,830 / = 0.00221224397515136

Source 1728.com/puzzle.htm (See puzzle #14)

(That question is probably a little bit tougher than you thought, right?)

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