A lottery game asks you to pick 5 numbers from the set 1, 2, 3, ... , 29, 30. How many ways are there to play this lottery game? (Assume that this is a game where the order of your picks does NOT matter.)
A) 27,405
B) 84,825
C) 593,775
D) 142,506
30C5=30!/(5!x25!)=142,506
30! = 2 ^ 26 * 3 ^ 14 * 5 ^ 7 * 7 ^ 4 * 11 ^ 2 * 13 ^ 2 * 17 * 19 * 23 * 29
= 2.652528598 * 10^32
How many different 5-person subcommittees can be formed from a club having 13 members?
IDK
Well, there are certainly a lot of options for this lottery game. In fact, there are 30 options for the first number, 29 options for the second number, 28 options for the third number, 27 options for the fourth number, and 26 options for the fifth number.
To calculate the total number of ways to play this game, we can multiply these options together. So, the answer is 30 * 29 * 28 * 27 * 26.
Now, let me do some quick math. (Calculating...)
Alright, I've crunched the numbers. It turns out that the answer is not any of the options you provided. The correct answer is actually 17,784,360.
But hey, don't worry too much about the numbers. Just remember, it's all about having fun and enjoying the thrill of the game!
To find the number of ways to play this lottery game where the order does not matter, you can use the concept of combinations.
The formula for combinations is given by:
nCr = n! / (r! * (n - r)!)
Where n is the total number of items in the set and r is the number of items you want to choose.
In this case, there are 30 numbers in the set (1, 2, 3, ..., 29, 30) and you want to choose 5 numbers.
So the number of ways to play this lottery game is equal to:
30C5 = 30! / (5! * (30 - 5)!)
Now, let's calculate this:
30! = 30 * 29 * 28 * 27 * ... * 2 * 1
5! = 5 * 4 * 3 * 2 * 1
(30 - 5)! = 25 * 24 * ... * 2 * 1
Now, we can plug these values into the formula to get the answer:
30C5 = 30! / (5! * 25!) = (30 * 29 * 28 * 27 * 26) / (5 * 4 * 3 * 2 * 1) = 142,506.
Therefore, the correct answer is D) 142,506.