maths

The number of arrangements of five letters from the word 'magnetic' that contain the word net is:

a)60 b)100 c)360 d)630 e)720

we're still doing this at school and I still don't get it; since I have to use three of the eight letters I only have five left and can only use two of them, so should I multiply 8 by 5?

asked by Audrey
  1. This problem is a permutation problem. The hint is given in the word "arrangement." However, you could make this to a combination problem by multiplying by r! (since nCr=(nPr)/r! and multiplying it to r! would give you nPr). To do this problem, you have how many can you choose from? (that would be your n) and how many do you choose? (that would be your r)

    8 C 3 (8 choose 3)
    To enter it in the graphing calculator, you enter 8, cPr, then 3. Changing it into permutation, multiply the result by 3!.

    posted by Anonymous
  2. what is the question asking specifically?

    posted by Anonymous
  3. treat "net" as if it were one item
    eg. let X="net"

    so now you are simply arranging the X plus 2 of the remaining 5 letters.

    Put the X first, then the other two places can be filled in 5x4 ways, which is 20 ways

    But the X, the "net" could also be in the middle, or at the end, so there are 3 ways for the X to go

    the number of ways is then 3x5x4 = 60

    or

    Since the X (the "net") now makes your letters spell MAGXIC, which is 5 letters, and we have to fill 3places, the number of ways = 5x4x3 = 60

    posted by Reiny
  4. how many possible combinations there were and thank you very much for your explanation :)

    posted by Audrey
  5. oh, okay, wow, so that's the metohd; I get it now; thanks!
    before I had no idea how to even set up the equation, but I'm strating to see the pattern!
    :D

    posted by Audrey
  6. I get where the five is coming from, since that's the remainder of letters, but where are you getting the four from?

    posted by Audrey
  7. let's pretend we put the X down first, which is really the "net" occupying 3 letter positions
    That leaves 2 more positions to be filled from the remaining 5 letters, the MAGIC.
    So there are 5 ways to fill the next position, right?
    Since we must have picked one of those 5 letters, that would leave 4 letters remaining for the next and last spot.

    Hence the 5x4, I multiplied by 3 because the "net" could have been first, in the middle or at the end

    Hope that makes sense

    e.g. Suppose I want to make all possible arrangements consisting of 4 letters, those 4 letters coming from the word COMPUTER, with no letter appearing more than once

    no. of arrangements = 8x7x6x5 = 1680

    posted by Reiny
  8. oh, okay!
    thanks a million! :)

    posted by Audrey

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