If nPr = 5040 and nCr = 42 then find n and r.
If nPr = 5040 and nCr = 42 then find n and r. Correct Answer 7, 5
Given, nPr = 5040 and nCr = 42. nPr = n! / (n – r)!. nCr = n! / r!(n – r)!. In order to find n and r we have to divide nPr with nCr. nPr / nCr = 5040 / 42 = 120. r! = 120. Hence r = 5, now n! / (n – 5)! = 5040. n(n – 1)(n – 2)(n – 3)(n – 4)(n – 5)(n – 6) = 7 * 6 * 5 * 4 * 3 * 2 * 1