Question

In a particular state's lottery, the jackpot is given out by successfully picking five "regular" numbersranging from 1-24 and four "wild card” numbers ranging from 1-10. You cannot use the samenumber twice in a category. What is the probability of winning this state's lottery with purchasingjust 1 ticket?

Answer 1

`(1)/(8925840)`

Explanation:

To determine the probability we must calculate the following number of combinations:

Combination formula:

`_nC_r=(n!)/(r!(n-r)!)`

Number of ways of selecting 5 numbers out of 24 is C(24, 5)

`_(24)C_5=(24!)/(5!\cdot(24-5)!)=42504`

Number fo ways of selecting 4 numbers out of 10 is C(10, 4):

`_(10)C_4=(10!)/(4!\cdot(10-4)!)=210`

So number of ways of selecting five numbers is:

`42504*210=8925840`

Out of these possible ways, one one is for jackpot so

`p(\text{jackpot)}=(1)/(8925840)`