powerball lottery. the powerball lottery is played twice each week in 44 states, the district of columbia, and the virgin islands. to play powerball, a participant must purchase a ticket, select five numbers from the digits 1 through and then select a powerball number from the digits 1 through to determine the winning numbers for each game, lottery officials draw 5 white balls out a drum of 69 white balls numbered 1 through 69 and 1 red ball out of a drum of 26 red balls numbered 1 through to win the powerball jackpot, a participant's numbers must match the numbers on the 5 white balls in any order and must also match the number on the red powerball. the numbers with a powerball number of 10 provided the record jackpot of billion (powerball website). a. how many powerball lottery outcomes are possible? (hint: consider this a two-step random experiment. select the 5 white ball numbers and then select the 1 red powerball number.) b. what is the probability that a lottery ticket wins the powerball lottery?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
powerball lottery. the powerball lottery is played twice each week in 44 states, the district of columbia, and the virgin islands. to play powerball, a participant must purchase a ticket, select five numbers from the digits 1 through and then select a powerball number from the digits 1 through to determine the winning numbers for each game, lottery officials draw 5 white balls out a drum of 69 white balls numbered 1 through 69 and 1 red ball out of a drum of 26 red balls numbered 1 through to win the powerball jackpot, a participant's numbers must match the numbers on the 5 white balls in any order and must also match the number on the red powerball. the numbers with a powerball number of 10 provided the record jackpot of billion (powerball website). a. how many powerball lottery outcomes are possible? (hint: consider this a two-step random experiment. select the 5 white ball numbers and then select the 1 red powerball number.) b. what is the probability that a lottery ticket wins the powerball lottery?
a.
Obtain the total number of outcomes in the Powerball lottery.
It is given that there are 69 white balls, each numbered from 1 to 69, and 26 red balls, each numbered from 1 to 26.
The participant has to choose 5 white balls out of 69 white balls, and 1 red ball out of 26 red balls.
The number of ways to choose 5 white balls out of 69 white balls is calculated as follows:
The number of ways to choose 1 red ball out of 26 red balls is 26.
The total number of outcomes in the Powerball lottery is calculated as follows:
Thus, the total number of outcomes in the Powerball lottery is 292,201,338.
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