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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 the monitor be selected if the monitor must be a boy? What is the answer if the monitor must be a girl?
Evaluate: 8! – 6!
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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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Find n, if `1/("n"!) = 1/(4!) - 4/(5!)`
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Find n if: `("n"!)/(3!("n" - 5)!) : ("n"!)/(5!("n" - 7)!)` = 10:3
Show that
`("n"!)/("r"!("n" - "r")!) + ("n"!)/(("r" - 1)!("n" - "r" + 1)!) = (("n" + 1)!)/("r"!("n" - "r" + 1)!`
Find the value of: `(5(26!) + (27!))/(4(27!) - 8(26!)`
Show that: `((2"n")!)/("n"!)` = 2n(2n – 1)(2n – 3)....5.3.1
Five balls are to be placed in three boxes, where each box can contain up to five balls. Find the number of ways if no box is to remain empty.
A hall has 12 lamps and every lamp can be switched on independently. Find the number of ways of illuminating the hall.
A question paper has 6 questions. How many ways does a student have if he wants to solve at least one question?
