to win a certain lottery game, a player must correctly choose 4 numbers from the numbers 1 - 25. numbers…

to win a certain lottery game, a player must correctly choose 4 numbers from the numbers 1 - 25. numbers cannot repeat. what is the probability of winning this lottery? note: enter the answer as a fraction in simplest form. ex. 3/4 for 6/8.

to win a certain lottery game, a player must correctly choose 4 numbers from the numbers 1 - 25. numbers cannot repeat. what is the probability of winning this lottery? note: enter the answer as a fraction in simplest form. ex. 3/4 for 6/8.

Answer

Explanation:

Step1: Calculate total number of combinations

The formula for combinations is $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n = 25$ and $r=4$. So $C(25,4)=\frac{25!}{4!(25 - 4)!}=\frac{25!}{4!×21!}=\frac{25\times24\times23\times22}{4\times3\times2\times1}=12650$.

Step2: Determine number of winning combinations

There is only 1 winning combination (since there is only one correct set of 4 - numbers).

Step3: Calculate probability

Probability $P=\frac{\text{Number of winning combinations}}{\text{Total number of combinations}}=\frac{1}{12650}$.

Answer:

$\frac{1}{12650}$