AP EAMCET202021 Sep 2020Morning ShiftMathematicsPermutation and CombinationActual
If ( ^n C_r ) denotes the number of combinations of ' (n ) ' things taken ' (r ) ' at a time, then the expression ( ^n C_ r+1 + ^n C_ r-1 +2^n C_r ) equals
Options
- A( ^ n+2 C_r )
- B( n+2 r+1 )
- C( ^ n+1 C_r )
- D( n+1 r+1 )
Correct answer
B. ( n+2 r+1 )
Step-by-step solution
( aligned ^n C_ r+1 & + ^n C_ r-1 +2^n C_r & = ( ^n C_r+ ^n C_ r+1 )+ ( ^n C_r+ ^n C_ r-1 ) & = n+1 r+1 + ^ n+1 C_r= n+2 r+1 aligned ) Hence, option (b) is correct.