How many ways can the word math be arranged?

whats the answer

1 Answer
Aviv S.
Apr 25, 2018

There are #24# different ways to arrage the letters in the word #"math"#.

Explanation:

Think about it like this:

If you pick any letter (#"m, a, t,"# or #"h"#) for the first "letter slot" in the word, there are four different choices.

Then, for the next "slot", you have three other letters to choose from to put in there, so that triples the combinations. That's already #4*3# possible ways, or #12#.

For the third slot, you only have two other letters to choose from, so that doubles the combinations, making it #24#.

Finally, for the last slot, you only have one letter to choose from, so that multiplies the combinations by #1#, keeping it at #24#.

(Also, if you understand Python, you can easily make a computer figure this out for you using two lines:

But for school purposes, that's probably considered cheating.)

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