C webwork.uml.edu/weows ructures-1-Section-203 Chapter 2 review: Problem 8 Prev
ID: 3145210 • Letter: C
Question
C webwork.uml.edu/weows ructures-1-Section-203 Chapter 2 review: Problem 8 Prev Up Next 2 pts) There are 5 juniors and 4 seniors in a class. (a) How many groups of four people contain at least one senior? Answer: (b) How many groups contain at least one senior? In this part, a group could contain anywhere from one to 9 students.) Answer: Hint: For part (a), answer the following questions first: - How many groups of four people are there? - How many groups of four people don't contain at least one senior? Use a similar hint for part (b) Note: You can earn partial credit on this problem.Explanation / Answer
a)1 Senior & 3 Junior = 4C1*5C3 ={4!/(1!*3!)}*{5!/(3!*2!)} = 40
2 Senior & 2 Junior = 4C2 *5C2 ={ 4!/(2!*2!}*{5!/(2!*3!)} =60
3 Senior & 1 Junior = 4C3* 5C1 = {4!/(3!*1!)}*{5!/(1!*4!)} =20
4 Senior & 0 Junior = 4C4 = 4!/(0!*4!) = 1
Total no of group = 121
b) Total number of group having atleat one people = 9C1+9C2+9C3+9C4+9C5+9C6+9C7+9C8+9C9 =427
Number of group having no Senior = 5C1+5C2+5C3+5C4+5C5 = 31
Group having atleat one senior = 427-31 =396
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