Q) Total number of permutation of "K" different things in a row taken not more than "r " at a time (each thing may be repeated any number of times ) is equal to
left parenthesis A right parenthesis k to the power of r minus 1 space space space left parenthesis B right parenthesis k to the power of r space space space space left parenthesis C right parenthesis fraction numerator k to the power of r minus 1 over denominator k minus 1 end fraction space space space space left parenthesis D right parenthesis fraction numerator k left parenthesis k to the power of r minus 1 right parenthesis over denominator k minus 1 end fraction

Asked by araima2001 | 6th Apr, 2017, 06:34: AM

Expert Answer:

begin mathsize 16px style When space we space arrange space one space things space at space straight a space time comma space the space number space of space possible space permutations space is space straight k.
When space we space arrange space them space two space at space straight a space time space the space number space of space possible space permutations space are space straight k cross times straight k equals straight k squared
and space so space on. space Thus space the space total space number space of space permutations space are
straight k plus straight k squared plus straight k cubed plus....... straight k to the power of straight r equals fraction numerator straight k open parentheses straight k to the power of straight r minus 1 close parentheses over denominator straight k minus 1 end fraction space space space space space space space space space open parentheses For space straight n greater than 1 close parentheses
end style

Answered by Sneha shidid | 6th Apr, 2017, 09:31: AM