If ^n P_r=30240 and ^n C_r=252 , then the ordered pair (n, r) is equal to

Step-by-step solution

Given that, ^n P_r=30240 and ^n C_r=252 aligned & n ! (n-r) ! =30240 and n ! (n-r) ! r ! =252 & r != 30240 252 =120 & r=5 & n ! (n-5) ! =30240 & aligned aligned & n(n-1)(n-2)(n-3)(n-4)=30240 & n(n-1)(n-2)(n-3)(n-4) & =10(10-1)(10-2)(10-3)(10-4) & n=10 aligned Hence, required ordered pair is (10,5) .