Question

How many different samples of size 3 can be taken from a finite population of size 10?

Answer 1

120 different samples can be taken.


`_(10)C_3=(10!)/(3!7!) = 120`

Answer 2

A combination is a selection of part from a set of objects. In a combination the order of selecting object does not matters.

So we use combination for selecting 3 from the population of 10

We know combination of selecting 'r' objects from 'n' is nCr

`nCr = (n!)/(r!(n-r)!)`

We need to find 10C 3

`10C3 = (10!)/(3!(10-3)!)`

`= (10!)/(3!7!)`

= 120

120 different samples of size 3 can be taken from a finite population of size 10