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  • The sum of the series <img alt="\binom{10}{0}\binom{10}{4}+\binom{10}{1}\binom{10}{5}+\binom{10}{2}\binom{10}{6}+...+\binom{10}{6}\binom{10}{10}" src="http://entrancecorner.oncodecogs.com/gif.

The sum of the series \binom{10}{0}\binom{10}{4}+\binom{10}{1}\binom{10}{5}+\binom{10}{2}\binom{10}{6}+...+\binom{10}{6}\binom{10}{10} is

Option: 1

\binom{20}{6}


Option: 2

\binom{20}{7}


Option: 3

\binom{20}{8}


Option: 4

\binom{20}{9}


Answers (1)

best_answer

\\\binom{10}{0}\binom{10}{4}+\binom{10}{1}\binom{10}{5}+\binom{10}{2}\binom{10}{6}+...+\binom{10}{6}\binom{10}{10} \\\\=\binom{10}{0}\binom{10}{6}+\binom{10}{1}\binom{10}{5}+\binom{10}{2}\binom{10}{4}+...+\binom{10}{6}\binom{10}{0}\,\,\,\,\,\\\\(Using\,\,\,^nC_r = ^nC_{n-r}) \\\\\text{Now upper indices are constant and sum of lower indices is constant} \\=\binom{10+10}{6} \\\\=\binom{20}{6}

 

Posted by

Ritika Kankaria

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