Question 1179204: Hi! Please help me with this question! Thank you so much!
What are the odds of winning the power ball? Show all work for full credit. (Note: In power ball, there are 49 white balls in which 5 are chosen. Then one of 42 red balls is chosen.) Please show work and explain if it is not a hassle.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Absolutely! Let's break down how to calculate the odds of winning the Powerball lottery.
**1. Calculating the Odds of Choosing the White Balls:**
* We need to choose 5 white balls out of 49.
* This is a combination problem, as the order in which the balls are drawn doesn't matter.
* The formula for combinations is: nCr = n! / (r! * (n-r)!)
* Where n is the total number of items, and r is the number of items to choose.
* So, the number of ways to choose 5 white balls from 49 is:
* ⁴⁹C₅ = 49! / (5! * 44!) = (49 * 48 * 47 * 46 * 45) / (5 * 4 * 3 * 2 * 1) = 1,906,884
**2. Calculating the Odds of Choosing the Red Powerball:**
* We need to choose 1 red ball out of 42.
* This is a simple combination:
* ⁴²C₁ = 42! / (1! * 41!) = 42
**3. Calculating the Total Odds of Winning:**
* To win the Powerball jackpot, you need to match all 5 white balls AND the red Powerball.
* To get the total odds, we multiply the number of ways to choose the white balls by the number of ways to choose the Powerball:
* 1,906,884 * 42 = 80,089,128
**4. Expressing the Odds:**
* The odds of winning the Powerball jackpot are 1 in 80,089,128.
**Explanation:**
* The combination formula (nCr) is used because the order of the white balls drawn doesn't matter. Matching the same 5 numbers in any order wins.
* We multiply the possibilities of the white balls and the red ball because these are independent events; both need to occur for a jackpot win.
* The odds are extremely high against winning the jackpot, which is typical for large lotteries.
**Therefore, the odds of winning the Powerball are 1 in 80,089,128.**
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