Q1. How many different ways can the letters of \"statistics\" be arranged? Q2. I

Question

Q1. How many different ways can the letters of "statistics" be arranged?

Q2.

In designing an experiment involving a treatment applied to 5 test subjects, researchers plan to use a simple random sample of 5 subjects selected from a pool of 30 available subjects. (Recall that with a simple random sample, all samples of the same size have the same chance of being selected.) Answer the questions below.

a. How many different simple random samples are possible?

b. What is the probability of each simple random sample in this case?

Explanation / Answer

(1) There are total 10 letters in the word "statistics". Hence possible arrangements are 10!.

However there are 3 s, 3 t and 2 i, this means we need to remove those arragements. Hence total different arrangements are 10! / (3! * 3! * 2!) = 50400

(2)

(a) 5 subjects from a pool of 30 available subjects can be selected in 30C5 ways.

Hence total different random samples possible are 30C5 = 142506

(b) As the sampling is random, hence every subject has equal probability of getting selected.

Required probability = 1/142506

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