Twelve people attend the first meeting of the Star Wars Club. They exchange e-mail addresses. How many exchanges take place?

What is C(12,2) ?

I think he's got it !

To determine how many exchanges take place when twelve people exchange email addresses, we can use a combination formula.

The formula for finding the number of combinations is:

n! / (r!(n - r)!)

Where n is the total number of people and r is the number of people exchanging email addresses at a time.

In this case, all twelve people need to exchange email addresses, so r = 12.

Plugging these values into the formula, we get:

12! / (12!(12 - 12)!)

Simplifying further:

12! / (12! * 0!)

Since 0! (the factorial of zero) is equal to 1, we can simplify further:

12! / 12!

The factorial of 12 is:

12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

So:

(12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)

Simplifying further, we find:

1

Therefore, only 1 exchange takes place when twelve people exchange email addresses.

To find the number of exchanges that take place, we need to determine how many unique pairs of people can be formed from a group of twelve.

Since the order in which the pair exchanges e-mail addresses doesn't matter (e.g., the exchange between person A and person B is the same as person B and person A), we can use the concept of combinations to solve this problem.

The formula for calculating combinations is given by C(n, r) = n! / (r!(n-r)!), where n is the total number of items, and r is the number of items selected at a time.

In this case, we have twelve people, and we need to select two at a time to form a pair. Applying the combination formula, we get:

C(12, 2) = 12! / (2!(12-2)!)
= 12! / (2!10!)
= (12 * 11 * 10!) / (2! * 10!)

Now, let's simplify the equation:

C(12, 2) = (12 * 11) / 2!
= (12 * 11) / (2 * 1)
= 132 / 2
= 66

Therefore, there will be 66 exchanges that take place at the first meeting of the Star Wars Club.