Question

In the New Jersey Pick 6 lottery game, a bettor selects six different numbers, each between 1 and 49. Winning the top prize requires that the selected numbers match those that are drawn, but the order does not matter. Do calculations for winning this lottery involve permutations or combinations? Why?

Answer 1

Explanation:

There are 6 numbers through which one can win lottery

There are total of 49 numbers from 1 to 49

Total no of ways to select 6 numbers out of 49 number

`=^(49)C_(6)`

No of ways in which 6 numbers can be chosen out of 6 winning numbers
`=^6C_6`

Probability
`=(favorable)/(Possible\ outcome)`

`P=(^6C_6)/(^(49)C_(6))`

`P=(6!)/(49* 48* 47* 46* 45* 44)`

`P=(1)/(13983816)`

It involves combination because we have to choose the correct numbers for winning