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

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anonymous
  • anonymous
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?
anonymous
  • anonymous
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.
anonymous
  • anonymous
Why doesn't John choose 3?
anonymous
  • anonymous
Because he can't do something like wear 3 shirts and call that an outfit.
anonymous
  • anonymous
Oh, I see. Oh, so should I do either 25C3 or 25P3 ?
anonymous
  • anonymous
No, it is not a complicated problem like that. It's just multiplication.
anonymous
  • anonymous
Oh, okay. So just (3)(10)(12) = 360 ?
anonymous
  • anonymous
The only detail that is important is if he can do something like NOT wear a necktie or NOT wear a suit.
anonymous
  • anonymous
because that would mean we'd have something like (3+1)(10+1)(12+1)
anonymous
  • anonymous
Okay, I'll remember that.
anonymous
  • anonymous
But if he must have all three, then yes, 360 is correct.
anonymous
  • anonymous
Okay, great - thanks so much! :D
campbell_st
  • 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...

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