Achiever math question

[CaliPreDent]

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Hey Guys,

I came across this question on achiever and the explanation was pretty weak so I was wondering if one of yall had a better explanation. The answer was 6 fyi and they said the way to solve it is by 3!, which makes no sense to me. Any help would be appreciated!

Your best colleague working only two days a week has already scheduled to have her lunch at two designated restarunats of the five eating places near your office. If you work five days a week, how many ways can you schedule your restaurant visits sot that you and your colleague can always have lunch together?

 

[Streetwolf]

Hey Guys,

I came across this question on achiever and the explanation was pretty weak so I was wondering if one of yall had a better explanation. The answer was 6 fyi and they said the way to solve it is by 3!, which makes no sense to me. Any help would be appreciated!

Your best colleague working only two days a week has already scheduled to have her lunch at two designated restarunats of the five eating places near your office. If you work five days a week, how many ways can you schedule your restaurant visits sot that you and your colleague can always have lunch together?

The colleague has already scheduled her lunch so there's nothing you can do about that. You HAVE to schedule those 2 days at those places to guarantee having lunch with her.

That leaves 3 other days with 3 other restaurants. There are 3! = 6 ways to schedule those days with those restaurants.

 

[CaliPreDent]

that's exactly what the solution had said....but I don't understand why you are looking at the other days...wouldn't she not have lunch on those other 3 days? I'm still confused...any other explanations!

 

[Streetwolf]

It asks how many ways YOU can schedule YOUR visits.

YOU have 5 restaurant visits a week.

For example you can go to A, B, C, D, and E in that order.
You could go to B, E, D, A, C in that order.
Etc.

The catch here is that your colleague works 2 days a week and has already picked her restaurants. Let's say she works Tuesday and Friday and picked D and A:

-, D, -, -, A

Now you HAVE to go to those two restaurants on those days in order to eat with her. How can you schedule the rest of your week?

B, D, C, E, A
B, D, E, C, A
C, D, B, E, A
C, D, E, B, A
E, D, B, C, A
E, D, C, B, A

It doesn't matter what days or what restaurants she picks because the counting begins AFTER that's been established. Notice how in those 6 cases the D is ALWAYS in the 2nd spot (Tuesday) and the A is ALWAYS in the 5th spot (Friday).

 

[CANgnome]

the question doesn't say that you cannot visit the same restaurant multiple times during the week does it? I know the answer is 6, suggesting that you cannot, but if i just out and read the question, I would have went with 5^3, 125 different ways, since you can visit the same restaurant as many times as you want.

 

[CaliPreDent]

Thanks! That makes perfect sense now!! Thank-you again!