Given:\(\frac{{^{10}{{\rm{P}}_{\rm{4}}}}}{{^{10}{{\rm{C}}_{\rm{4}}}}}\)Formula used:\(^nP_r = \frac{n!}{(n-r)!}\)\(^nC_r = \frac{n!}{r!(n-r)!}\)Calculation:? \(\frac{{^{10}{{\rm{P}}_{\rm{4}}}}}{{^{10}{{\rm{C}}_{\rm{4}}}}}\) = \(\frac{{\frac{10!}{(10-4)!}}}{\frac{10!}{4!(10-4)!}}\)? \(\frac{{^{10}{{\rm{P}}_{\rm{4}}}}}{{^{10}{{\rm{C}}_{\rm{4}}}}}\) = \(\frac{1}{\frac{1}{4!}}\)? \(\frac{{^{10}{{\rm{P}}_{\rm{4}}}}}{{^{10}{{\rm{C}}_{\rm{4}}}}}\) = 4!? \(\frac{{^{10}{{\rm{P}}_{\rm{4}}}}}{{^{10}{{\rm{C}}_{\rm{4}}}}}\) = 4 × 3 × 2 × 1 = 24? 24 is the required answer.Additional Information n! = n × (n -1) × ... × 0!0! = 1