In how many different ways can the letters of the word MAMMAL be rearranged so that the letters M are separated?
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"so that the letters M are separated"; that's the tricky part. The numerical answer is 72. I'm just not sure how to get to it... – Brendan Oct 14 '14 at 03:10
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Oh, my mistake. – Edward Jiang Oct 14 '14 at 03:16
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The number of arrangements of MAMMAL is $6!/3!/2!=60$, ignoring the restriction that no two $M$s be together, so the answer cannot be $72$ – Ross Millikan Oct 14 '14 at 03:37
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You have three $M$s that need to be placed in a line of six without being next to each other. You have a stars and bars problem. Start with three $M$s. Now pick two slots for the $A$s If they separate both pairs of $M$s, how many choices of places for the $L$? If one is on an end, how many choices for the $L$. If they are both on the end, how many choices for the $L$? If they are together in the middle, how many choices for the $L$? I think $72$ is badly wrong.
Ross Millikan
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