Question

(a) Count the number of ways to select a sample of 3 people to serve on a board of directors from a population of 6 people________. answer:
(b) If a simple random sampling procedure is to be employed, the chances that any particular sample will be the one selected are__________.

Answer 1

Answer:

(a) 20 ways

(b) 0.05 or 5%

Step-by-step explanation:

(a) Assuming that the order in which people are chosen does not matter, the number of ways to select 3 people out of possible 6 is given by the following combination.

$n=\frac{6!}{(6-3)!3!}=\frac{6*5*4}{3*2*1}=20\ ways$

(b) In a random sampling procedure, every outcome is just as likely to occur. Therefore, the chances that any particular sample will be the one selected are:

$C = \frac{1}{20}=0.05 = 5\%$

Answer 2

The question is an illustration of combination

• There are 20 ways to select the sample of 3 from 6
• The chances that any particular sample will be the one selected are 1/20

To select 3 people from a total of 6, we make use of the following combination formula

$^nC_r = \frac{n!}{(n - r)!r!}$

So, we have:

$^6C_3 = \frac{6!}{3!3!}$

Simplify

$^6C_3 = \frac{720}{36}$

Divide

$^6C_3 = 20$

This means that there are 20 ways to select the sample of 3 from 6

The chance that a set of 3 people is selected is:

p = 1/20

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