a production company is casting ten roles for a tv show that needs three men and seven women
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A play needs three protagonists (a man, a woman, and a girl), two antagonists (a man and a woman), and two supporting roles (a man and a boy). Six men, six women, three boys, and four girls attended the auditions. The number of ways the roles can be cast is:
Adi S.
$75-90$ Counting Principles Solve these exercises by using the appropriate counting principle(s). Casting a Play A group of 22 aspiring thespians contains 10 men and 12 women. For the next play, the director wants to choose a leading man, a leading lady, a supporting male role, a supporting female role, and eight extras - three women and five men. In how many ways can the cast be chosen?
Counting and Probability
Counting
Assume that there are 7 unfilled roles: 4 male and 3 female. There are 7 men and 5 women, including Mary, auditioning for a part in the play. (1) How many different casts are there? (2) How many of these casts include Mary?
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