## Related questions with answers

The Enormous State University’s Accounting Society has decided to produce a version of the ballet Swan Lake, in which all the female roles (including all of the swans) will be danced by men, and vice versa. Here are the main characters: Prince Siegfried. Prince Siegfried’s Mother. Princess Odette, the White Swan. The Evil Duke Rotbart. Odile, the Black Swan. Cygnet #1, young swan. Cygnet #2, young swan. Cygnet #3, young swan. The ESU Accounting Society has on hand a total of 4 female dancers and 12 male dancers who are to be considered for the main roles. How many possible casts are there?

Solution

VerifiedWe can build a cast in the following way:

Step 1. Choose a female dancer for Prince Siegfried. There are 4 possible choices.

Step 2. Choose a male dancer for Prince Siegfried's Mother. There are 12 possible choices.

Step 3. Choose a male dancer for Princess Odette. There are 11 possible choices.

Step 4. Choose a female dancer for Evil Duke Robart. There are 3 possible choices.

Step 5. Choose a male dancer for Odile. There are 10 possible choices.

Step 6. Choose a male dancer for Cygnet #1. There are 9 possible choices.

Step 7. Choose a male dancer for Cygnet #2. There are 8 possible choices.

Step 8. Choose a male dancer for Cygnet #3. There are 7 possible choices.

According to $\textbf{Multiplication Principle}$, there are

$4\times12\times11\times3\times10\times9\times8\times7 = 7,923,360$

possible casts.

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