Question

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."

Answer 1

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.

Answer 2

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

Answer 3

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.

Answer 4

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?

Answer 5

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.

Answer 6

Why doesn't John choose 3?

Answer 7

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

Answer 8

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

Answer 9

No, it is not a complicated problem like that.

It's just multiplication.

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

Okay, I'll remember that.

Answer 14

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

Answer 15

Okay, great - thanks so much! :D

Answer 16

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...