The number of different simple random samples of size 4 that can be obtained from a population of size 44 is 135,751.
This can be calculated using the combination formula:
nCr = n! / (r! * (n-r)!)
where:
n is the population size (44 in this case)
r is the sample size (4 in this case)
Plugging in the values, we get:
44C4 = 44! / (4! * (44-4)!)
= 44 * 43 * 42 * 41 / (24 * 20)
= 135,751
Therefore, there are 135,751 different simple random samples of size 4 that can be obtained from a population of size 44.