There are subsets of {1, 2, 3, ..., n} that contain 5 numbers. 1/4 of that would be and "1/4 of the five element subsets of (1,2,3...n) contain the element 7" implies that must be an integer.
Yes, there is enough information given to solve for .
HallsofIvy has told you that 1/4 of the number of subsets containing 5 elements is:
Now, to find the number of subsets of cardinality 5 containing 7 as an element, we may use the fundamental counting principle to state:
Hence, we have:
Now, you just need to solve for .