The odds of winning the Megamillions jackpot is 1M Players p

The odds of winning the Megamillions jackpot is 1/M. Players pick six numbers from two separate pools of numbers - five different numbers from 1 to 75 and one number from 1 to 15. The odds of winning the Powerball jackpot is 1/N where five numbers are drawn out of a drum with 59 numbers and one number is drawn from 35 numbers.

a. Determine M and N.
b. Which has the better odds? Why?

I am very lost, please provide an explanation on how to approach and solve these kinds of problems!

Solution

a)

For megamillions:

There are 75C5 = 17259390 ways to choose 5 numbers.

Also, there are 15 ways to choose another number from 1 to 15.

Thus, there are 17259390*15 = 258890850 ways to choose in megamillions.

Hence, M = 258890850. [answer]

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For powerball:

There are 59C5 = 5006386 ways to choose 5 numbers.

Also, there are 35 ways to choose another number from 1 to 35.

Thus, there are 5006386*35 = 175223510 ways to choose in powerball.

Hence, N = 175223510. [answer]

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B)

As we can see, POWERBALL has better odds, as there is less options to choose from, hence, a higher probability of winning.