Chapter 18: Probability 249Now, if you’re willing to do laundry often so everything is wearable, you could wear a different
outfit every day for almost two months with just those few items. Add a couple of sweaters, and
you’d be set for almost four months.
2543120
sweaters shirts slacks shoes outfits3335So what about that lottery ticket? Let’s suppose you can’t repeat numbers, but you do have to
have them in the right order. The basic counting principle says you can multiply the number of
options you have for each choice to find the total number of ways to pick five numbers from the
pool of fifty.
50 49 48 47 46254,251,200That’s over 250 million different ways to pick five numbers, and only one will win.CHECK POINT
Your favorite salad bar has 2 kinds of greens, 5 different veggie toppings, 3 crunchy
toppings, and 4 dressings. How many different salads can you make if you choose...- Greens and a dressing?
- Greens, a veggie, and a dressing?
- Greens, a veggie, a crunchy topping, and a dressing?
- Greens, 2 different veggies, and a dressing?
- Greens, 2 different veggies, 2 crunchy toppings, and a dressing?
Permutations
A popular television game show has a game in which the contestant is told all the digits in the
price of the very expensive prize (usually a car or a trip), but the contestant only wins the prize
if he or she can put the digits in the correct order. Depending on how many digits there are, the
chance of guessing correctly may be pretty good or pretty terrible.
If I told you that the digits in the price of your prize are 3 and 6, you’re either going to guess 36
or 63. There are only two possible answers, and one of them is right. Basic counting principle
says 2 choices for the first digit times 1 choice for the second digit gives you two possibilities.
But you’re not going to find a car for $36 or for $63. There will be quite a few digits in the price
of the car or trip or other expensive prize. How many possibilities would there be if you had to
put 5 digits in order? Or 6 digits?