Question

Suppose population size is 1000 and you want samples of size 997. How many samples can be made of that size?

Answer 1

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Answer 2

Given:

Total size of population= 1000

desired no. of sample size to be made= 997

To find:

How many samples can be made of the size 997.

Solution:

The sample can be made to 997 by choosing 997 people from the sample of 1000 people.

• Population size= 1000
• Sample size to be made = 997

In this way 3 people will be left out each time. Now by permutation and combination we can find the ways of choosing 997 people from 1000 people.

• no. of ways by which we can select 997 people out of 1000 people= 997 C 100.

1000 C 997= 1000!/ {997! * (1000-997)!}

= 1000! / 997!*3!

= (1000*999*998) / (3*2*1)

= 166,167,000

Therefore the no. of ways possible to make a sample size of 997 out of 1000 will be 166,167,000.