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?

Respuesta :

ANSWER:

[tex]\frac{1}{8925840}[/tex]

STEP-BY-STEP EXPLANATION:

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

Combination formula:

[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex]

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

[tex]_{24}C_5=\frac{24!}{5!\cdot(24-5)!}=42504[/tex]

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

[tex]_{10}C_4=\frac{10!}{4!\cdot(10-4)!}=210[/tex]

So number of ways of selecting five numbers is:

[tex]42504*210=8925840[/tex]

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

[tex]p(\text{jackpot)}=\frac{1}{8925840}[/tex]