Advertisements
Advertisements
Question
Show that: `((2"n")!)/("n"!)` = 2n(2n – 1)(2n – 3)....5.3.1
Solution
L.H.S. = `((2"n")!)/("n"!)`
`= ((2"n")(2"n"-1)(2"n"-2)(2"n"-3)(2"n"-4) ...6xx5xx4xx3xx 2xx1)/("n"!)`
`=((2"n")(2"n" - 1)[2("n" - 1)](2"n" - 3)[2("n" - 2)]...(2xx3)xx5xx(2xx2)xx3xx(2xx1)xx1)/("n"!)`
`=(2^"n"["n"("n"-1)("n"-2)....3.2.1][(2"n"-1)(2"n"-3)...5.3.1])/("n"!)`
= `(2^"n"("n"!)(2"n"-1)(2"n"-3)...5.3.1)/"n!"`
= 2n(2n −1)(2n −3)...5.3.1
= R.H.S.
APPEARS IN
RELATED QUESTIONS
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?
Evaluate: 6!
Evaluate: 8! – 6!
Compute: `(12!)/(6!)`
Compute: `(9!)/(3! 6!)`
Compute: `(6! - 4!)/(4!)`
Write in terms of factorial:
5 × 6 × 7 × 8 × 9 × 10
Write in terms of factorial:
6 × 7 × 8 × 9
Write in terms of factorial:
5 × 10 × 15 × 20 × 25
Find n, if `"n"/(6!) = 4/(8!) + 3/(6!)`
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: `((2"n")!)/(7!(2"n" - 7)!) : ("n"!)/(4!("n" - 4)!)` = 24:1
Find the value of: `(5(26!) + (27!))/(4(27!) - 8(26!)`
A hall has 12 lamps and every lamp can be switched on independently. Find the number of ways of illuminating the hall.
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.
