Question

9) There are 130 people at a meeting. Theyeach give a Valentine's Day card toeveryone else. How many cards weregiven?

Answer 1

Given that there are a total of 130 people at the meeting and each gives a Valentine's Day card to everyone else, you need to use the Permutation Formula in order to calculate the number of cards that were given:

$_nP_r=\frac{n !}{(n-r) !}$

Where "n" is the total number of objects in the set, and "r" is the number of objects selected from the set.

In this case, you can identify that:

$\begin{gathered} n=130 \\ r=2 \end{gathered}$

(Notice that the value of "r" is 2 because they give a card to each other).

Then, substituting values into the formula and evaluating, you get:

$\begin{gathered} _{130}P_2=\frac{130!}{(130-2)!} \\ \\ _{130}P_2=\frac{130!}{128!} \end{gathered}$$_{130}P_2=16770$

Hence, the answer is:

$16770\text{ }cards$