Advertisements
Advertisements
प्रश्न
Show that
`("n"!)/("r"!("n" - "r")!) + ("n"!)/(("r" - 1)!("n" - "r" + 1)!) = (("n" + 1)!)/("r"!("n" - "r" + 1)!`
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?
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?
How many five-digit numbers formed using the digit 0, 1, 2, 3, 4, 5 are divisible by 3 if digits are not repeated?
Evaluate: 8! – 6!
Compute: `(12!)/(6!)`
Compute: `(12/6)!`
Compute: (3 × 2)!
Compute: `(9!)/(3! 6!)`
Write in terms of factorial:
5 × 6 × 7 × 8 × 9 × 10
Write in terms of factorial:
3 × 6 × 9 × 12 × 15
Find n, if `1/("n"!) = 1/(4!) - 4/(5!)`
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
A student passes an examination if he/she secures a minimum in each of the 7 subjects. Find the number of ways a student can fail.
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?
