7 44-element subsets containing the letter a can be formed from the set {a,b,c,d,e,f,g}.
C(n,k) = n!/(k!(n-k)!)
Where n is the size of the set and k is the size of the subset.
In this case, n is 7 (the size of the set {a,b,c,d,e,f,g}) and k is 44. When these values are added to the formula, we obtain:
C(7,44) = 7!/(44!(7-44)!) = 7!/44! = 7
This means that there are 7 44-element subsets containing the letter a that can be formed from the set {a,b,c,d,e,f,g}.
Note that the combination formula only works when k is less than or equal to n. If k is greater than n, the result is always 0. In this case, the result is not 0 because k (44) is less than n (7).
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