AP EAMCET202125 Aug 2021Evening ShiftMathematicsPermutation and CombinationActual
If 8 ^7 P_r=7 ^8 P_ r-1 , what is the value of r ?
Options
- A3 and 4
- B2 and 5
- C4 and 5
- DNo solution (No such r exists)
Correct answer
D. No solution (No such r exists)
Step-by-step solution
8 ^7 P_r=7 ^8 P_ r-1 aligned & 8 7 ! (7-r) ! =7 8 ! 8-(r-1) ! & 8 ! (7-r) ! = 7 8 ! (9-r) ! & 1 (7-r) ! = 7 (9-r)(8-r) (7-r) ! & 1= 7 72-9 r-8 r+r^2 & r^2-17 r+72-7=0 & r^2-17 r+65=0 & r= 17 (17)^2-4 65 2 aligned which is not a natural number. Hence, there is no solution.