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प्रश्न
Write in terms of factorial:
5 × 6 × 7 × 8 × 9 × 10
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उत्तर
5 × 6 × 7 × 8 × 9 × 10 = 10 × 9 × 8 × 7 × 6 × 5
Multiplying and dividing by 4!, we get
= `(10 xx 9 xx 8 xx 7 xx 6 xx 5 xx 4!)/(4!)`
= `(10xx9xx8xx7xx6xx5xx4xx3xx2xx1)/(4!)`
= `(10!)/(4!)`
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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?
Compute: `(12!)/(6!)`
Compute: 3! × 2!
Compute: `(9!)/(3! 6!)`
Compute: `(8!)/(6! - 4!)`
Compute: `(8!)/((6 - 4)!)`
Write in terms of factorial:
3 × 6 × 9 × 12 × 15
Write in terms of factorial:
6 × 7 × 8 × 9
Find n, if `"n"/(6!) = 4/(8!) + 3/(6!)`
Find n, if (n + 1)! = 42 × (n – 1)!
Find n, if (n + 3)! = 110 × (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: `(9!)/(3!6!) + (9!)/(4!5!) = (10!)/(4!6!)`
Show that: `((2"n")!)/("n"!)` = 2n(2n – 1)(2n – 3)....5.3.1
