In how many ways can a person choose 3 movies to see in a theater playing 11

Just start at the beginning and think it through choice by choice.

There are 11 to choose from. How many can you choose? 11.

Now you've seen one. Choose another. How many do you have to choose from? 10, 'cos you've already seen one.

So how many ways can we choose 2 movies from 11? If the order matters, as for example if you have to see Movie 1 before Movie 2: The Sequel, then there would be 11 * 10 ways, but from your question, that's not the case here, so seeing Movie 1, and then Movie 2, or the other way around counts as one case; both ways you've seen Movies 1 and 2. So we need to divide that 11 * 10 by (1 * 2) which are the number of orders in which we can see them.

For three movies, as can choose from 11, then 10, then 9, but again since order doesn't matter, we need to divide that answer by the number of orders in which we could see those movies, which is (1 * 2 * 3).

Well, let's do some math (but not too serious, I promise). To figure out the number of ways a person can choose 3 movies to see out of 11 options, we can use a nifty formula called "combination."

Here's the formula: nCr = n! / (r! * (n - r)!)

Now, let's calculate it together. Plug in the values, thinking of choosing movies as picking distinct flavors of ice cream:

11C3 = 11! / (3! * (11 - 3)!)

11C3 = 11! / (3! * 8!)

Now, you might be wondering, what in the world is factorial? It's just a fancy way of multiplying numbers together.

So, let's break it down:

11! = 11 * 10 * 9 * 8! (because 11! = 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)

Now, let's plug it all back in:

11C3 = (11 * 10 * 9 * 8!) / (3! * 8!)

And voila! The 8! in the numerator and denominator cancels out:

11C3 = (11 * 10 * 9) / (3 * 2 * 1)

Finally, let's simplify it:

11C3 = (11 * 10 * 9) / 6

11C3 = 165

So, there are 165 ways for a person to choose three movies out of 11 options. That's a whole lot of popcorn to eat and movies to enjoy!

To find the number of ways a person can choose 3 movies from a set of 11, we can use the combination formula. The combination formula is:

C(n, r) = n! / (r!(n-r)!)

where n is the total number of items and r is the number of items we want to choose.

In this case, n = 11 (the total number of movies) and r = 3 (the number of movies to be chosen).

Using the combination formula, we can calculate:

C(11, 3) = 11! / (3!(11-3)!)
= 11! / (3!8!)
= (11 * 10 * 9 * 8!) / (3! * 8!)
= (11 * 10 * 9) / 3!
= (11 * 10 * 9) / 3 * 2 * 1
= 165

Therefore, there are 165 ways a person can choose 3 movies to see in a theater playing 11.

To calculate the number of ways a person can choose 3 movies out of 11, we can use the concept of combinations.

The formula for combinations is nCr, where n represents the total number of items to choose from, and r represents the number of items to choose.

In this case, n is 11 (the number of movies playing) and r is 3 (the number of movies to choose).

So, the number of ways to choose 3 movies from 11 can be calculated using the formula:

11C3 = 11! / (3! * (11-3)!)

Let's break down the calculation step-by-step:

1. Calculate 11 factorial (11!):
11! = 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

2. Calculate 3 factorial (3!):
3! = 3 * 2 * 1

3. Calculate (11-3) factorial ((11-3)!):
(11-3)! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

4. Substitute the values into the formula:
11C3 = 11! / (3! * (11-3)!)
= (11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / ((3 * 2 * 1) * (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1))

5. Simplify the expression:
11C3 = (11 * 10 * 9) / (3 * 2 * 1)
= 165

Therefore, there are 165 different ways a person can choose 3 movies to see in a theater playing 11.