Show that: 9!3!6!+9!4!5!=10!4!6! - Mathematics and Statistics

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Sum

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!xx6 xx 5!) + (9!)/(4 xx 3!  xx 5!)`

= `(9!)/(5!3!) [1/6 + 1/4]`

= `(9!)/(5! xx 3!)[(4 + 6)/(6xx4)]`

= `(9!xx10)/(6xx5!xx4xx3!)`

= `(10!)/(6!4!)`

= `(10!)/(4!6!)`

= R.H.S.

Concept: Concept of Factorial Function
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Chapter 6: Permutations and Combinations - Exercise 6.2 [Page 76]

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Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.2 | Q 12 | Page 76
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