Advertisements
Advertisements
प्रश्न
Show that
`("n"!)/("r"!("n" - "r")!) + ("n"!)/(("r" - 1)!("n" - "r" + 1)!) = (("n" + 1)!)/("r"!("n" - "r" + 1)!`
Advertisements
उत्तर
L.H.S = `("n"!)/("r"!("n" - "r")!) + ("n"!)/(("r" - 1)!("n" - "r" + 1)!)`
`=("n"!)/("r"("r" - 1)!("n" - "r")!) + ("n"!)/(("r" - 1)! xx ("n" - "r" + 1)("n" - "r")!`
= `("n"!)/(("r" - 1)!("n" - "r")!) [1/"r" + 1/("n" - "r" + 1)]`
= `("n"!)/(("r" - 1)!("n" - "r")!) [("n" - "r" + 1 + "r")/("r"("n" - "r" + 1))]`
= `("n"!.("n" + 1))/["r"("r" - 1)!("n" - "r" + 1)("n" - "r")!)`
= `(("n" + 1)!)/("r"!("n" - "r" + 1)!]` = R.H.S.
APPEARS IN
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?
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?
How many three-digit numbers can be formed using the digits 2, 3, 4, 5, 6 if digits can be repeated?
If numbers are formed using digits 2, 3, 4, 5, 6 without repetition, how many of them will exceed 400?
Evaluate: 8!
Evaluate: 8! – 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:
3 × 6 × 9 × 12 × 15
Evaluate: `("n"!)/("r"!("n" - "r"!)` For n = 12, r = 12
Find n, if `1/("n"!) = 1/(4!) - 4/(5!)`
Find the value of: `(8! + 5(4!))/(4! - 12)`
Find the value of: `(5(26!) + (27!))/(4(27!) - 8(26!)`
Show that: `((2"n")!)/("n"!)` = 2n(2n – 1)(2n – 3)....5.3.1
A question paper has 6 questions. How many ways does a student have if he wants to solve at least one question?
