AP EAMCET202119 Aug 2021Evening ShiftMathematicsPermutation and CombinationActual
For 1 ≤ r ≤ n , 1 r + 1 P r + 1 n - P r + 1 ( n - 1 ) is equal to
Options
- An P n
- Bn − 1 P r
- Cn P n + 1
- D0
Correct answer
B. n − 1 P r
Step-by-step solution
Using P r n = n ! n - r ! we get, 1 r + 1 P r + 1 n - P r + 1 ( n - 1 ) = 1 r + 1 n ! n - r - 1 ! - n - 1 ! n - r - 1 - 1 ! = 1 r + 1 n ! - n - r - 1 n - 1 ! n - r - 1 ! = 1 r + 1 n - 1 ! n - n + r + 1 n - r - 1 ! = n - 1 ! n - r - 1 ! = P r n - 1