Justify your answers, and why you use each formula. DO NOT SKIP STEPS, EVEN SIMP

Question

Justify your answers, and why you use each formula.
DO NOT SKIP STEPS, EVEN SIMPLE STEPS.

A class contains 22 girls and 18 boys. For all parts of this question, each boy and girl are distinguishable from one another. Answer the following questions: In how many ways can a committee of one boy and one girl be chosen? In how many ways can a committee of five students be chosen? In how many ways can a committee of two girls and three boys be chosen? In how many ways can a committee of five students be chosen such that all the students on the committee are the same sex? In how many ways can the girls and boys form a line where no two boys are standing next to one another? How many committees of five students contain at least two girls?

Explanation / Answer

a. select one boy from 18 boys and one girl from 22 girls so=> 18C1 * 22C1= 18 * 22 =396

b. commitee of 5 student can be chossed from 40(18+22) available is =22C5 = 22!/5! * 17! = 22*21*20*19*18/120

=>22*21*19*18/6=22*21*19*3 = 462*57=26334

c. select 2 girls from 22 girlas and 3 boys from 18 boys = 22C2 * 18C3 = 22!/2!*20! * 18!/3!*15!

11*21 * 3*17*16=188496

d. either select 5 boys from 18 boys or select 5 girls from 22 girls = 18C5+22C5 (Calculate it)

e. first arrange girls in 22! ways now we have 23 gaps available now select 18 gaps from 23 available gaps and arrange boys in 18! ways

22! * 23C18 * 18!(calculate it)

f. here 2G3B or 3G2B OR 4G1B OR 5G

SO 22C2*18C3 + 22C3*18C2 + 22C4*18C1 + 22C5 (Calculate it)

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