Question

Using the experimental sampling strategy, how many samples of size 4 (n = 4) can be drawn from the following population sizes?

(a) N = 6

(b) N = 7

(c) N = 8

(d) N = 9

Answer 1

Solution:

Let n be the sample size.

N be the population size.

The number of possible samples is _NC_n =   

(C denotes combination)

a)

N = 6

n = 4

_NC_n = N!/{n! * (N - n)! } = ₆C₄ = 6!/{4! * (6 - 4)! } = 15

15 samples are possible.

b)

N = 7

n = 4

_NC_n = N!/{n! * (N - n)! } = ₇C₄ = 7!/{4! * (7 - 4)! } = 35

35 samples are possible.

c)

N = 8

n = 4

_NC_n = N!/{n! * (N - n)! } = ₈C₄ = 8!/{4! * (8 - 4)! } = 70

70 samples are possible.

d)

N = 9

n = 4

_NC_n = N!/{n! * (N - n)! } = ₉C₄ = 9!/{4! * (9 - 4)! } = 126

126 samples are possible.