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Rearrange the ACE icon with repeated symbols

A student wishes to re-arrange the letters and asterisks on the icon shown. Given that the letters of the word ACE must be together in the clockwise manner, find the number of possible arrangements if (i) the asterisks must be separated, (ii) the positions of the letters and asterisks are labelled.

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Eleven symbols around a ring, clockwise from S at the top: S,D,F,F,G,G, asterisk,A,C,E, asterisk. Exactly one each of A,C,E,S,D; two F, two G, two asterisks. The question requires A,C,E together in that clockwise order.
Eleven symbols around a ring, clockwise from S at the top: S,D,F,F,G,G, asterisk,A,C,E, asterisk. Exactly one each of A,C,E,S,D; two F, two G, two asterisks. The question requires A,C,E together in that clockwise order.
Eleven symbols around a ring, clockwise from S at the top: S,D,F,F,G,G, asterisk,A,C,E, asterisk. Exactly one each of A,C,E,S,D; two F, two G, two asterisks. The question requires A,C,E together in that clockwise order.

CJC · Lecture · Example 19

Decide whether order matters and repetition is allowed; then count stages or disjoint cases.

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