Math Destroyer Question

[Mr. Thirsty]

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Math destroyer, Test 4, # 26 and 27. why in 26 does order matter whereas in number 27 order does not matter?

26.) A theater has 5 doors. In how many ways can an actor enter one door and leave through a different door?

27.) A piece of paper has 10 distinct dots drawn on it. If a pair of dots determines a line, how many different ways are there to draw a line on this paper?

Chad did a great job explaining when order matters and when it does not; and I understand how to calculate between the two, but for some reason I cannot grasp the concept with these two examples.

Can someone explain this to me? Any 'for-sure method' out there to check whether order matters that I can apply to problems like these?

Thanks in advance! 😀

 

[theleatherwalle]

I hate QR questions like this

26: I think the first answer is 20. I just drew this out and thought about it.

27: For the second answer it is a combination. 10!/2!*8!. Look up combination and permutations.

I may be wrong.

 

[StudentDoc1234]

For question #27 Math Destroyer Test #4... I think understand why it would be 10!/2! (because there are 2 selections out of 10 possibilities, right?) but why do we also multiply the denominator by 8!?

 

[ToBeDDSS]

Look up the formula for combination.
nCr = n!/(n-r)!*r!
10C2 = 10!/(10-2)!*2! = 10!/(8!*2!)
Hope this helps

 

[PocketRocket]

26) The number of options for the first door is 5, the number of options for the second door to go through is 4, therefore; you multiply 5 x 4 to get 20 ways. The reason why order matters here is this: You have 5 doors, A B C D E. If you go through door A and then go through door B you have gone 1 way. Going through door B and THEN through door A is another way. If you consider every possible combination you will end up with 20 ways to enter through one door and exit through another.

27) The reason why here order does NOT matter is because, unlike in the previous example where going through door A and then B is different from going through door B first and then A, here drawing a line from point A to point B will yield the same line as B to A. This is why you first do the same calculation as you would in #26, but then you have to account for the duplicates (segment AB=BA) by dividing by the "number of selections or points"! or 2!. So here, the number of choices for the beginning of a segment here is 10 and the number of choices to connect it to is 9. You multiply, 10 x 9 which gives you 90 ways to draw a segment where duplicates are not accounted for. Now we just divide by 2! and get 45 as the final answer.

 

[StudentDoc1234]

26) The number of options for the first door is 5, the number of options for the second door to go through is 4, therefore; you multiply 5 x 4 to get 20 ways. The reason why order matters here is this: You have 5 doors, A B C D E. If you go through door A and then go through door B you have gone 1 way. Going through door B and THEN through door A is another way. If you consider every possible combination you will end up with 20 ways to enter through one door and exit through another.

27) The reason why here order does NOT matter is because, unlike in the previous example where going through door A and then B is different from going through door B first and then A, here drawing a line from point A to point B will yield the same line as B to A. This is why you first do the same calculation as you would in #26, but then you have to account for the duplicates (segment AB=BA) by dividing by the "number of selections or points"! or 2!. So here, the number of choices for the beginning of a segment here is 10 and the number of choices to connect it to is 9. You multiply, 10 x 9 which gives you 90 ways to draw a segment where duplicates are not accounted for. Now we just divide by 2! and get 45 as the final answer.

That makes it so clear for me thank you!

 

[Tallon]

#27, order doesn't matter, however, this is like taking 2 people to a movie from 10 friends. Order doesn't matter, but you only have 2 spots. The question reads, "A pair of dots equals a line. How many different ways can you DRAW A LINE?" Or how many ways can you choose 2 of your 10 friends to go to a movie. The 8! should be left out and doesn't need to be there, if you can only fill 2 spots to make a line you have 10*9/2*1 after reducing you have 9*5 = 45. I hope that helps.