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Home / Doubts and Solutions/JEE/Mathematics

ncr+ncr-1=n+1cr

 

Asked by 154706865169453 2nd January 2018, 3:49 PM
Answered by Expert
Answer:
begin mathsize 16px style LHS equals fraction numerator straight n factorial over denominator straight r factorial left parenthesis straight n minus straight r right parenthesis factorial end fraction plus fraction numerator straight n factorial over denominator left parenthesis straight r minus 1 right parenthesis factorial left parenthesis straight n minus straight r plus 1 right parenthesis factorial end fraction equals fraction numerator straight n factorial over denominator straight r left parenthesis straight r minus 1 right parenthesis factorial left parenthesis straight n minus straight r right parenthesis factorial end fraction plus fraction numerator straight n factorial over denominator left parenthesis straight r minus 1 right parenthesis factorial left parenthesis straight n minus straight r plus 1 right parenthesis left parenthesis straight n minus straight r right parenthesis factorial end fraction equals space fraction numerator straight n factorial over denominator left parenthesis straight r minus 1 right parenthesis factorial left parenthesis straight n minus straight r right parenthesis factorial end fraction open parentheses 1 over straight r plus fraction numerator 1 over denominator left parenthesis straight n minus straight r plus 1 right parenthesis end fraction close parentheses equals fraction numerator straight n factorial over denominator left parenthesis straight r minus 1 right parenthesis factorial left parenthesis straight n minus straight r right parenthesis factorial end fraction open parentheses fraction numerator straight n plus 1 over denominator straight r left parenthesis straight n minus straight r plus 1 right parenthesis end fraction close parentheses equals fraction numerator left parenthesis straight n plus 1 right parenthesis factorial over denominator straight r factorial left parenthesis straight n minus straight r plus 1 right parenthesis factorial end fraction space equals to the power of straight n plus 1 end exponent straight C subscript straight r end style
Answered by Expert 9th January 2018, 12:08 PM
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