Question

winning the jackpot in a particular lottery requires that you select the correct four numbers between 1 and 55 and, in a separate drawing, you must also select the correct single number between 1 and 21. find the probability of winning the jackpot. the probability of winning the jackpot is (type an integer or simplified fraction)

Explanation:

Step1: Calculate number of ways to choose 4 numbers from 55

The number of combinations of choosing $r$ items from $n$ items is given by the formula $C(n,r)=\frac{n!}{r!(n - r)!}$. Here, $n = 55$ and $r=4$. So, $C(55,4)=\frac{55!}{4!(55 - 4)!}=\frac{55\times54\times53\times52}{4\times3\times2\times1}=341055$.

Step2: Calculate number of ways to choose 1 number from 21

There are 21 ways to choose 1 number from 21, i.e., $C(21,1)=\frac{21!}{1!(21 - 1)!}=21$.

Step3: Calculate total number of possible outcomes

The total number of possible outcomes for the lottery is the product of the number of ways to choose 4 - number combination and 1 - number combination. So, the total number of possible outcomes is $341055\times21 = 7162155$.

Step4: Calculate probability

The probability of winning the jackpot is the reciprocal of the total number of possible outcomes. So the probability $P=\frac{1}{7162155}$.

Answer:

$\frac{1}{7162155}$