velocity

Asked by varshitchouhan8 | 8th May, 2022, 08:48: PM

Expert Answer:

Suppose k objects have been chosen out of the n dissimilar objects.   Then we have to choose n−k objects from out of the two other sets. 

The choices would go like 0 from the first set and (n−k) from the other, or 1 from set 1 and (n−k−1) from the other etc.

This gives n−k+1 choices. 

sum from k equals 0 to n of left parenthesis n minus k plus 1 right parenthesis open parentheses table row n row k end table close parentheses equals sum from k equals 0 to n of left parenthesis n plus 1 right parenthesis open parentheses table row n row k end table close parentheses minus sum from k equals 0 to n of k open parentheses table row n row k end table close parentheses
space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals left parenthesis n plus 1 right parenthesis 2 to the power of n space minus space n space 2 to the power of n minus 1 end exponent
space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space left parenthesis n plus 2 right parenthesis 2 to the power of n minus 1 end exponent

Answered by Renu Varma | 9th May, 2022, 07:50: PM

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