Question

Here is a list of the main characters in Shakespeare's Romeo and Juliet. The first seven characters are male and the last four are female.

Escalus, prince of Verona
Paris, kinsman to the prince
Romeo, of Montague Household
Mercutio, friend of Romeo
Benvolio, friend of Romeo
Tybalt, nephew to Lady Capulet
Friar Lawrence, a Franciscan
Lady Montague, of Montague Household
Lady Capulet, of Capulet Household
Juliet, of Capulet Household
Juliet's Nurse

A total of 13 male and 9 female actors are available to play these roles. How many possible casts are there? (All roles are to be played by actors of the same gender as the character.)

Answer 1

Here, we are given that, for Shakespeare's Romeo and Juliet we have various roles.

There are 7 male and 4 female characters available.

And we have a total of 13 male and 9 female actors available.

We have to tell how many possible casts are there.

Notice that, here the characters are different , so the order is important.

So, Here, we use the concept of Permutations.

The possible casts for Male are given as

( 13 P 7 ) = 8,648,640 possible casts .

Further, the possible casts for Female are given as

( 9 P 4 ) = 3,024 possible casts.

So, finally, we have total possible casts are

( 13 P 7 ) * ( 9 P 4 )

= ( 8,648,640 )* ( 3,024 )

= 26,153,487,360

Hence, in all , there are total 26,153,487,360 possible casts.

This answers your question.

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