Rework problem 35 from the Chapter 2 review exercises in your text, involving auditioning for a...

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Rework problem 35 from the Chapter 2 review exercises in yourtext, involving auditioning for a play. For this problem, assume 13males audition, one of them being Karthikey, 7 females audition,one of them being Tiffany, and 5 children audition. The castingdirector has 4 male roles available, 2 female roles available, and1 child role available.
(1) How many different ways can these roles be filled from theseauditioners?
(2) How many different ways can these roles be filled if exactlyone of Karthikey and Tiffany gets a part?
(3) How many different ways can these roles be filled if at leastone of Karthikey and Tiffany gets a part?
(4) What is the probability (if the roles are filled at random) ofboth Karthikey and Tiffany getting a part?

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GivenNumber of male persons for audition 13Number of female persons for audition 7Number of children for audition 5ANSWER1There are 4 male roles available so the casting director has tochoose 4 persons out of the 13 male persons available and this canbe done in waysThere are 2 female roles available so the casting director hasto choose 2 persons out of the 7 female persons available and thiscan be done in waysThere are 1 child role available so the casting director has tochoose 1 child out of the 5 children available and this can be donein waysWe have to look at all the possible combinations available forthe 7 people selectedSo the number of different ways these roles can befilled139475254175075 waysANSWER2We have to consider two casesCase I If Karthikey is selected forthe role and Tiffany is not selected for the See Answer

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