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Chapter 5: Problem 48

In how many ways can a sample (without replacement) of 5 items be selected from a population of 15 items?

Short Answer

Expert verified
There are 3003 different ways to select a sample of 5 items from a population of 15 items without replacement.

Step by step solution

01

Understanding Combinations

In this context, a combination is a selection of items without regard for the order in which they are selected. The number of combinations of N items taken r at a time is given by the formula: \[C(N, r) = \frac{N!}{r!(N-r)!}\] where ! represents factorial and is a function applied to natural numbers.
02

Applying the Formula

In this particular problem, N or the total number of items in the population is 15, and r, the number of items to be selected in the sample, is 5. Substituting these values into the formula gives: \[C(15, 5) = \frac{15!}{5!(15-5)!}\]
03

Calculating the Result

Carrying out these operations, \[= \frac{15!}{5!(10)!}\] = \[= \frac{1307674368000}{120*3628800}\] = 3003

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Most popular questions from this chapter

Suppose the owner of a salvage company is considering raising a sunken ship. If successful, the venture will yield a net profit of \(\$ 10\) million. Otherwise, the owner will lose \(\$ 4\) million. Let \(p\) denote the probability of success for this venture. Assume the owner is willing to take the risk to go ahead with this project provided the expected net profit is at least \(\$ 500,000\). a. If \(p=.40\), find the expected net profit. Will the owner be willing to take the risk with this probability of success? b. What is the smallest value of \(p\) for which the owner will take the risk to undertake this project?

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