Advertisements
Advertisements
Question
Show that `(9!)/(3!6!) + (9!)/(4!5!) = (10!)/(4!6!)`
Advertisements
Solution
L.H.S. = `(9!)/(3!6!) + (9!)/(4!5!)`
= `(9!)/(3! xx 6 xx 5!) + (9!)/(4 xx 3! xx 5!)`
= `(9!)/(3!5!)[1/6 + 1/4]`
= `(9!)/(3!5!)[(4 + 6)/(6 xx 4)]`
= `(10 xx 9!)/(6 xx 5! xx 4 xx 3!)`
= `(10!)/(6!4!)`
= `(10!)/(4!6!)`
= R.H.S.
APPEARS IN
RELATED QUESTIONS
Evaluate: 8!
Evaluate: 10! – 6!
Compute: `(12!)/(6!)`
Compute: `(9!)/(3! 6!)`
Compute: `(8!)/(6! - 4!)`
Write in terms of factorial.
3 × 6 × 9 × 12 × 15
Write in terms of factorial.
6 × 7 × 8 × 9
Write in terms of factorial.
5 × 10 × 15 × 20
Evaluate : `("n"!)/("r"!("n" - "r")!)` for n = 8, r = 6
Evaluate : `("n"!)/("r"!("n" - "r")!)` for n = 12, r = 12
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: `((17 - "n")!)/((14 - "n")!)` = 5!
Find n, if: `("n"!)/(3!("n" - 3)!) : ("n"!)/(5!("n" - 5)!)` = 5 : 3
Find n, if: `("n"!)/(3!("n" - 3)!) : ("n"!)/(5!("n" - 7)!)` = 1 : 6
Show that `("n"!)/("r"!("n" - "r")!) + ("n"!)/(("r" - 1)!("n" - "r" + 1)!) = (("n" + 1)!)/("r"!("n" - "r" + 1)!)`
Show that `((2"n")!)/("n"!)` = 2n (2n – 1)(2n – 3) ... 5.3.1
Simplify `(("n" + 3)!)/(("n"^2 - 4)("n" + 1)!)`
Simplify `1/("n"!) - 1/(("n" - 1)!) - 1/(("n" - 2)!)`
Simplify `("n" + 2)/("n"!) - (3"n" + 1)/(("n" + 1)!)`
Simplify `1/(("n" - 1)!) + (1 - "n")/(("n" + 1)!)`
Simplify `1/("n"!) - 3/(("n" + 1)!) - ("n"^2 - 4)/(("n" + 2)!)`
Simplify `("n"^2 - 9)/(("n" + 3)!) + 6/(("n" + 2)!) - 1/(("n" + 1)!)`
Select the correct answer from the given alternatives.
In how many ways 4 boys and 3 girls can be seated in a row so that they are alternate
Select the correct answer from the given alternatives.
Find the number of triangles which can be formed by joining the angular points of a polygon of 8 sides as vertices.
Eight white chairs and four black chairs are randomly placed in a row. The probability that no two black chairs are placed adjacently equals.
