A bookshelf contains 6 different Java programming books and 5 different C++ book

Question

A bookshelf contains 6 different Java programming books and 5 different C++ books. Suppose that 4 books are to be selected.

a. How many ways can 4 books be drawn from the combined set of 11 books on the bookshelf if the order in which the books drawn is important?

b. How many ways can 4 books be drawn from the combined set of 11 books on the bookshelf if order is ignored?  

c. How many ways can 2 C++ books and 2 Java books be drawn? Ignore order.

d. If the 4 books are randomly drawn from the bookshelf, what is the probability that exactly 1 C++ book will appear in the sample?

Explanation / Answer

a. The number of ways 4 books can be drawn from a combined set of 11 books (ordering is important, that is first JAVA, then C++) is P(11,4)=11!/(11-4)!=7920 ways.

b. The number of ways 4 books can be drawn from a combined set of 11 books (ordering is not important) is C(11,4)=11!/4!(11-4)!=330 ways.

c. 2 C++ books can be drawn out of 5 in 5C2 ways, and 2 JAVA books can be drawn out of 6 in 6C2 ways.

Therefore, 2 C++ and 2 JAVA books can be drawn is 5C2*6C2 ways=10*15=150 ways.

d. This accounts for binomial distribution, with number of trials, n=11, probability of success, p=5/11, and specific number of success in 11 trials, is r=1. Use P(X,r)=nCr(p)^r(1-p)^n-r.

P(X=1)=4C1(5/11)^1(1-5/11)^3=0.2995.

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