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प्रश्न
Show that: `(9!)/(3!6!) + (9!)/(4!5!) = (10!)/(4!6!)`
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उत्तर
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.
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संबंधित प्रश्न
A teacher wants to select the class monitor in a class of 30 boys and 20 girls. In how many ways can he select a student if the monitor can be a boy or a girl?
Evaluate: 6!
Compute: `(12!)/(6!)`
Compute: `(12/6)!`
Compute: 3! × 2!
Compute: `(8!)/((6 - 4)!)`
Write in terms of factorial:
5 × 6 × 7 × 8 × 9 × 10
Write in terms of factorial:
6 × 7 × 8 × 9
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Evaluate: `("n"!)/("r"!("n" - "r"!)` For n = 12, r = 12
Find n, if `"n"/(8!) = 3/(6!) + 1/(4!)`
Find n, if (n + 1)! = 42 × (n – 1)!
Find n if: `("n"!)/(3!("n" - 5)!) : ("n"!)/(5!("n" - 7)!)` = 10:3
Find n, if: `((15 - "n")!)/((13 - "n")!)` = 12
Show that
`("n"!)/("r"!("n" - "r")!) + ("n"!)/(("r" - 1)!("n" - "r" + 1)!) = (("n" + 1)!)/("r"!("n" - "r" + 1)!`
Show that: `((2"n")!)/("n"!)` = 2n(2n – 1)(2n – 3)....5.3.1
How many quadratic equations can be formed using numbers from 0, 2, 4, 5 as coefficient if a coefficient can be repeated in an equation.
