AP EAMCET20227 Jul 2022Evening ShiftMathematicsPermutation and CombinationActual
If ^n P_r= ^ (n-1) P_r+x^ (n-1) P_ (r+1) , n, r N and r n , then x=
Options
- A(n+1)
- B(r+1)
- Cn
- Dr
Correct answer
D. r
Step-by-step solution
aligned ^n P_r- & ^ n-1 P_r= n ! (n-r) ! - (n-1) ! (n-r-1) ! & = (n-1) ! (n-r-1) ! ( n n-r -1 )= (n-1) ! (n-r) ! r & = (n-1) ! ((n-1)-(r-1) ! r=r ^ n-1 P_ r-1 ^n P_r & = ^ n-1 P_r+r ^ n-1 P_ r-1 x & =r aligned