LyraElizabethAdams 3 years ago I need some help, please! :) . . . "Explain why the following sentences are INCORRECT: John has 3 suits, 10 shirts, and 12 neckties.  He will need to buy some more clothes if he wants to come to work each work day in a different outfit for a whole year."

1. wio

We can assume that an outfit would just be the combination of a suit, shirt, and necktie. When tasks are done in parallel (you must do one task or the other), then their sum is the total number of combinations. When tasks are done in sequence (you must do all tasks), then their product is the total number of combinations.

2. wio

In this case, it is a sequence of tasks. So we multiply the number of ways to do the task.

3. wio

The only ambiguity here is if he can go to work without a tie, shirt, or suit. In that case, we could add 1 to each task.

Okay, I do understand that part. Here's where I'm confused, though. Should I do: (3)(10)(12) = 360? or should it be 360C3 (because you have a total of 360 choices, but you can only choose 3 per day?

5. wio

It is NOT 360 choose 3. We would use 360 choose 3 if he had 360 articles of clothing, and any combination of 3 articles is an outfit.

Why doesn't John choose 3?

7. wio

Because he can't do something like wear 3 shirts and call that an outfit.

Oh, I see. Oh, so should I do either 25C3 or 25P3 ?

9. wio

No, it is not a complicated problem like that. It's just multiplication.

Oh, okay. So just (3)(10)(12) = 360 ?

11. wio

The only detail that is important is if he can do something like NOT wear a necktie or NOT wear a suit.

12. wio

because that would mean we'd have something like (3+1)(10+1)(12+1)

Okay, I'll remember that.

14. wio

But if he must have all three, then yes, 360 is correct.

Okay, great - thanks so much! :D

16. campbell_st

ok by the fundamental theorem of counting John has 3 x 10 x 12 = 360 possible clothing combinations... assuming he works 365 days a year he is 5 combinations short...