AP EAMCET20224 Jul 2022Morning ShiftMathematicsPermutation and CombinationActual
The total number of permutations of n ( > 1 ) different things taken not more than r at a time, when each thing may be repeated any number of times is
Options
- An ( n n - 1 ) n - 1
- Bn r - 1 n - 1
- Cn ( n r - 1 ) n - 1
- DNone of these
Correct answer
C. n ( n r - 1 ) n - 1
Step-by-step solution
When we arrange one things at a time, the number of possible permutations is n . When we arrange them two at a time the number of possible permutations are n × n = n 2 and so on. Thus, the total number of permutations are n + n 2 + . . . . + n r = n ( n r - 1 ) n - 1 ( ∵ n > 1 )