How many different ways can an instructor select 2 textbooks from a possible 17?

Question

How many different ways can an instructor select 2 textbooks from a possible 17? 34 272 289 136 A bookcase contains 3 statistics books and 5 biology books. If 2 books are chosen at random, the chance that both are statistic books is 3/28 10/28 13 28/13 A university has 10.000 students of which 4000 are male and 6000 are female. If a class of 30 students is chosen at random from the university population, find the mean and variance of the number of male students. Mean = 15. Variance = 15 Mean = 12. Variance = 72 Mean = 9. Variance = 36 Mean = 72. Variance = 12.

Explanation / Answer

a) this is a simple combinations problem , using the formula nCr , where n = 17 and r = 2

so 17C2 = 17! / 2! * (17-2)! = 17*16/2 = 136

b) 3 stats books and 5 biology

2 books chosen at random , P that both books are statistics

so total books = 3+5 = 8 , so 2 books can be selected in 8C2 ways

2 books are chosen at random and both stats

so 2 booksk from 3 statistics books can be selected in 3C2 ways

required probability is thus , using the nCr formulae again ,

3C2/8C2 = 3/(8*7/2)= 3/28

c) 4000 males , 6000 females , total 1000 students

n = 30 students are selected at random

mean and variance of male students

so we know that

Proportion of males p = 0.4 as 4000/10000 , thus q = 1-p = 0.6
Mean of males = np = 0.4*30 = 12

sd of males = sqrt[npq] = sqrt[12*0.6] = 2.68, thus variance = 2.68*2.68 = 7.2

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