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Question
Show that `(9!)/(3!6!) + (9!)/(4!5!) = (10!)/(4!6!)`
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Solution
L.H.S. = `(9!)/(3!6!) + (9!)/(4!5!)`
= `(9!)/(3! xx 6 xx 5!) + (9!)/(4 xx 3! xx 5!)`
= `(9!)/(3!5!)[1/6 + 1/4]`
= `(9!)/(3!5!)[(4 + 6)/(6 xx 4)]`
= `(10 xx 9!)/(6 xx 5! xx 4 xx 3!)`
= `(10!)/(6!4!)`
= `(10!)/(4!6!)`
= R.H.S.
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