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The problem asks for the number of ways to choose y applicants from a pool of x. This is a standard combination problem:
xCy = 56

We need to determine if there exists an integer for each given such that the combination equals 56.

Statement I: - y=28
If y=28, the smallest possible value for x is 28.
28(C)28 = 1, 29(C)28 = 29, 30(C)28 = 435

The value skips right over 56. I is impossible.

Statement II: - y=55
Using the property : nC(n-1) = n
If we let x=56, then 56(C)55 = 56.
This matches our total. -> II is possible.

Statement III: - y=56
If , y=56 the smallest can be is 56.
56(C)56 = 1, 57(C)56 = 57

Again, the value 56 is never reached. ->III is impossible.
Only Statement II works.

Correct Answer: B
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