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!.
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
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