ana finds 11 shirts in his size at a clearence sale. How many different purchases could ana make?

the answer is 2047, any idea how to answer this? thanks!!

ok thanks!

To determine the number of different purchases Ana can make from the available 11 shirts, we need to consider the concept of combinations. In this case, we want to find the total number of combinations of choosing between 0 and 11 shirts, including all possibilities in between.

The formula to calculate combinations, also known as the binomial coefficient, is:

C(n, k) = n! / (k! * (n-k)!)

Where:
- C(n, k) represents the number of combinations of choosing k items from a set of n items,
- n! denotes the factorial of n (the product of all positive integers less than or equal to n),
- k! represents the factorial of k,
- (n-k)! denotes the factorial of (n-k).

Using this formula, we can calculate the number of different purchases Ana can make as follows:

C(11, 0) + C(11, 1) + C(11, 2) + ... + C(11, 11)

By summing the combinations for each possible value of k, ranging from 0 to 11.

Plugging in the values, we get:

C(11, 0) + C(11, 1) + C(11, 2) + ... + C(11, 11)
= 1 + 11 + 55 + 165 + 330 + 462 + 462 + 330 + 165 + 55 + 11 + 1
= 2047

Therefore, Ana can make a total of 2047 different purchases from the 11 shirts.

To find the answer, we need to calculate the total number of different purchases Ana can make using the 11 shirts.

Ana has 11 options for the first shirt, as she can choose any of the 11 shirts in her size. For the second shirt, she still has 11 options since she can choose any shirt regardless of what she chose before. Similarly, for the third shirt, she has 11 options, and so on.

To find the total number of different purchases, we need to multiply the number of options together for each shirt. In this case, since Ana has 11 choices for each of the 11 shirts, we multiply 11 by itself 11 times:

11 x 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11 = 22,275,668,156,160

Therefore, Ana can make 22,275,668,156,160 different purchases using the 11 shirts in her size. It is important to note that this number is an example of permutation, where the order matters.

11 multiplied by 186 is closest to 2047 as I can get.