Math  /  Discrete

QuestionHow many ways can the letters in MAXIMUM be arranged? Well, there are 7 letters, so that would be 7!7! if they were all different. But that counts MAXIMUM as a new arrangement (switching the M's around). To avoid recounting these "arrangements," note that every ordering appears 3!=63!=6 times because of the matching M's. To eliminate all those duplicates from consideration, divide by 3!. This reveals that there are actually 840 (7! divided by 3!) distinct permutations of the letters in MAXIMUM. Similarly, there would be 1260 (71 divided by 2121) different ways to arrange the letters in DOTPLOT. There would be 7!7! arrangements if they were all different, reduced by a factor of 21 for the matching O's and 2!2! for the matching Ts. Complete parts a through f below. a) How many ways can the letters in the word OHIO be arranged?
12 b) How many ways can the letters in the word ALASKA be arranged?
120 c) How many ways can the letters in the word MONTANA be arranged?
1260 d) How many ways can the letters in the word ARKANSAS be arranged? \square

Studdy Solution
Perform the division to find the number of distinct permutations:
4032012=3360 \frac{40320}{12} = 3360
The number of ways the letters in the word "ARKANSAS" can be arranged is:
3360 \boxed{3360}

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