Combinatorics??

quitaskinme wrote:There are 10 children in a company's day-cre center, and a pair of children is to be selected to play a game. At most, how many different pairs are possible?

A)100
B)90
C)50
D)45
E)25

Another approach:

Let's say that every child is paired with another child and those to children play the game.

After all of the games have been played, we ask each of the 10 children, "How many different people did you play with?"
We'll find that EACH CHILD played with 9 other children, which gives us a total of 90 games (since 10 x 9 = 90).

From here we need to recognize that every pair of children has been counted TWICE. For example, if Child A and Child B play a game together, then Child A counts it as a game, AND Child B also counts it as a game. Of course only one game occurred.

To account for the duplication, we'll divide 90 by 2 to get 45

Answer: D

Cheers,
Brent

Here's a related (and harder) question - https://www.beatthegmat.com/how-many-han ... 78283.html

Cheers,
Brent