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vbucks72
18.01.2020 •
Mathematics
Consider three classes, each consisting of n students. from this group of 3n students, a group of 3 students is to be chosen.
a. how many choices are possible?
b. how many choices are there in which all 3 students are in the same class?
c. how many choices are there in which 2 of the 3 students are in the same class and the other student is in a different class.
d. how many choices are there in which all 3 students are in different classes?
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Ответ:
Step-by-step explanation:
Given that there are three classes, each consisting of n students. From this group of 3n students, a group of 3 students is to be chosen.
a) Out of 3n students to draw 3 students we use combination since order does not matter.
Hence no of ways =![3nCn\\](/tpl/images/0460/4590/e1ac3.png)
b) If three students are to be in same class, either from I class or Ii or III
No of ways = nC3 + nc3+nc3 = 3(nC3)
c) 2 of the 3 students are in the same class and the other student is in a different class.
2 can be either from I or II or III and the remaining from any one of other classes.
So no of ways =![3(nC2) + 2nC1](/tpl/images/0460/4590/c4f5d.png)
d) in which all 3 students are in different classes
Each student 1 is selected from each class of n students
So![3(nC1) = 3n](/tpl/images/0460/4590/3c856.png)
Ответ:
its A.
Step-by-step explanation: