AP EAMCET201920 Apr 2019Morning ShiftMathematicsPermutation and CombinationActual
For (k > 0, _ x=0 ^ k^x x ! _ n n ! (n-x) ! (1- k n )^ n-x ( 1 n )^x= )
Options
- A0
- B(k )
- C(x )
- D1
Correct answer
D. 1
Step-by-step solution
( aligned & For k > 0, _ x=0 ^ k^x x ! _ n n ! (n-x) ! (1- k n )^ n-x ( 1 n )^x & = _ n _ x=0 ^n n ! x !(n-x) ! (1- k n )^ n-x ( k n )^x & = _ n _ x=0 ^n ^n C_x (1- k n )^ n-x ( k n )^x & = _ n (1- k n + k n )^n= _ n 1^n=1 aligned ) Hence, option (4) is correct.