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=(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=(130!)/((130-2)!) \\ \\ _(130)P_2=(130!)/(128!) \end{gathered}`
`_(130)P_2=16770`

Hence, the answer is:

`16770\text{ }cards`