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 7 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.) I have worked this out multiple times and just can\'t get it right...please help. I would like the solution as well as how you came to it if possible. Solution We need to combine a choice of 7 out of 13 possible male actors with a choice of 4 out of 7 possible female actors. 13C7 * 7C4 = [13! / (7! 6!)] * [7! / (4! 4!)] = [13*12*11*10*9*8 / (6*5*4*3*2*1)] * [7*6*5 / (4*3*2*1)] = 1716 * 8.75 = 15015 possible casts. .