pls get me a clear answer for the question: 61c57 - 60c56= 60c3

Asked by keerthanapradeep550 | 25th Mar, 2017, 07:27: PM

Expert Answer:

begin mathsize 16px style Using space straight C presuperscript straight n subscript straight r equals fraction numerator straight n factorial over denominator left parenthesis straight n minus straight r right parenthesis factorial straight r factorial end fraction
Consider comma space RHS equals straight C presuperscript 60 subscript 3
LHS
equals straight C presuperscript 61 subscript 57 minus straight C presuperscript 60 subscript 56
equals fraction numerator 61 factorial over denominator 57 factorial 4 factorial end fraction minus fraction numerator 60 factorial over denominator 56 factorial 4 factorial end fraction
equals fraction numerator 61 cross times 60 factorial over denominator 57 factorial cross times 4 cross times 3 factorial end fraction minus fraction numerator 60 factorial cross times 57 over denominator 57 cross times 56 factorial cross times 4 cross times 3 factorial end fraction
equals fraction numerator 61 cross times 60 factorial over denominator 57 factorial cross times 4 cross times 3 factorial end fraction minus fraction numerator 60 factorial cross times 57 over denominator 57 factorial cross times 4 cross times 3 factorial end fraction
equals fraction numerator 60 factorial over denominator 57 factorial 3 factorial end fraction open parentheses 61 over 4 minus 57 over 4 close parentheses
equals fraction numerator 60 factorial over denominator 57 factorial 3 factorial end fraction open parentheses 1 close parentheses equals fraction numerator 60 factorial over denominator 57 factorial 3 factorial end fraction equals straight C presuperscript 60 subscript 3 equals RHS
Hence space proved. end style

Answered by Rebecca Fernandes | 25th Mar, 2017, 09:26: PM