Maths · Meaning of P(n,r) and C(n,r)
If and then the ordered pair \) is equal to:
If \( ^{n} \boldsymbol{P}_{r}=\mathbf{3 0 2 4 0} \) and \( ^{n} \boldsymbol{C}_{r}=\mathbf{2 5 2}, \) then the ordered pair \( (n, r) \) is equal to:
- A. (12,6)
- B. (10,5)
- C. (9,4) (年. \( 9,4,4) \)
- D. (16,7)
Step-by-step solution
Given nPr = 30240 and nCr = 252. We know nPr = nCr * r!, so r! = 30240/252 = 120, giving r = 5. Then nC5 = 252, and solving nP5 = n(n-1)(n-2)(n-3)(n-4) = 30240 gives n = 10. Thus (n, r) = (10, 5).