Question

( 1- 1/6 )x ( 1- 1/7 ) (1-1/8) x(1-1/9 ) x(1-1/10)

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Answer 1

\(\left(1-\dfrac{1}{6}\right)\times\left(1-\dfrac{1}{7}\right)\times\left(1-\dfrac{1}{8}\right)\times\left(1-\dfrac{1}{9}\right)\times\left(1-\dfrac{1}{10}\right)\)

\(=\left(\dfrac{6}{6}-\dfrac{1}{6}\right)\times\left(\dfrac{7}{7}-\dfrac{1}{7}\right)\times\left(\dfrac{8}{8}-\dfrac{1}{8}\right)\times\left(\dfrac{9}{9}-\dfrac{1}{9}\right)\times\left(\dfrac{10}{10}-\dfrac{1}{10}\right)\)

\(=\dfrac{5}{6}\times\dfrac{6}{7}\times\dfrac{7}{8}\times\dfrac{8}{9}\times\dfrac{9}{10}\)

\(=\dfrac{5\times6\times7\times8\times9}{6\times7\times8\times9\times10}=\dfrac{5}{10}=\dfrac{1}{2}\)