20 (Ans)
set cardinality = n
Number of 5 element sets = nC5
Number of 5 element sets containing 7 = (n-1)C4 $\because$ we have to take 7 & from
remaining n-1 elements we have to take 4 elements}.
now , given in Question
$\frac{nC5}{4}$ = (n-1)C4
=> $\frac{n!}{4 * (n-5)! * 5! } = \frac{(n-1)!}{ (n-5)! * 4! }$
which gives n = 20 (Ans)