What about games that use only one die? Do you think any one number will
come up more often than another when you throw only one die? No, it
won’t. On one die, there are six numbers, so you have one chance out of
six (i) of getting any number. Thus, the chances are even for any
number to come up. If you rolled one die a thousand times, you would
find that each number would probably come up about the same number of
times.
Buttons and boxes
Suppose you have five buttons, each one a different color, and two
little boxes. How many ways can you combine the buttons in the two boxes
without repeating a combination?
Well, for one, you could put four buttons in one box and one button in
the other box. Then you could change that combination four times, just
by changing the button that’s by itself.
That’s five different combinations. But are there any other
combinations?
Yes, there are. Do you think you can figure them out? Get yourself five
buttons of different colors, or just some scraps of colored paper, and
try. You don’t really need boxes-just keep the two groups separated. Use
crayons and paper to keep a record of each combination. That way, you’ll
be sure you’re not repeating any combination.
Altogether, counting the five combinations already mentioned, there are
sixteen different ways to combine the five colored buttons in the two
boxes. After you’ve tried working out the combinations, you can check
your results against the pictures at the bottom of the page.
Here are the sixteen possible combinations. To make it easy to check
your answers, the buttons are numbered 1, 2, 3, 4, and 5.
