CBSE Class 11-science Answered

$F i n d space t h e space v a l u e space o f space C presuperscript n subscript r plus C presuperscript n subscript r minus 1 end subscript$ Please provide solution to this question

Asked by Topperlearning User | 08 Oct, 2016, 01:07: PM

Expert Answer

$C presuperscript n subscript r equals fraction numerator n factorial over denominator r factorial left parenthesis n minus r right parenthesis factorial end fraction C presuperscript n subscript r minus 1 end subscript equals fraction numerator n factorial over denominator left parenthesis r minus 1 right parenthesis factorial left parenthesis n minus r plus 1 right parenthesis factorial end fraction C presuperscript n subscript r plus C presuperscript n subscript r minus 1 end subscript equals fraction numerator n factorial over denominator r factorial left parenthesis n minus r right parenthesis factorial end fraction plus fraction numerator n factorial over denominator left parenthesis r minus 1 right parenthesis factorial left parenthesis n minus r plus 1 right parenthesis factorial end fraction equals fraction numerator n factorial over denominator left parenthesis r minus 1 right parenthesis factorial left parenthesis n minus r right parenthesis factorial end fraction open parentheses 1 over r plus fraction numerator 1 over denominator n minus r plus 1 end fraction close parentheses equals fraction numerator n factorial over denominator left parenthesis r minus 1 right parenthesis factorial left parenthesis n minus r right parenthesis factorial end fraction open parentheses fraction numerator n plus 1 over denominator r left parenthesis n minus r plus 1 right parenthesis end fraction close parentheses equals fraction numerator left parenthesis n plus 1 right parenthesis factorial over denominator r factorial left parenthesis n minus r plus 1 right parenthesis right parenthesis factorial end fraction equals C presuperscript n plus 1 end presuperscript subscript r$