The number of ways of selecting \(r\) objects from a set of \(n\) distinct objects is given by the combination formula:

\(^nC_r = \frac{n!}{r!(n-r)!}\)

In this case, you want to find the number of ways of selecting 6 out of 10 subjects, so \(n = 10\) and \(r = 6\).

\(^{10}C_6 = \frac{10!}{6!(10-6)!}\)

Calculating:

\(^{10}C_6 = \frac{10!}{6! \cdot 4!} = \frac{10 \cdot 9 \cdot 8 \cdot 7}{4 \cdot 3 \cdot 2 \cdot 1} = 210\)