Advertisements
Advertisements
Question
Evaluate: `("n"!)/("r"!("n" - "r"!)` For n = 8, r = 6
Solution
n = 8, r = 6
`("n"!)/("r"!("n" - "r"!)) = (8!)/(6!(8 - 6!))`
= `(8 xx 7 xx 6!)/(2!6!)`
= `(8 xx 7)/(2!)`
= `(8xx7)/(1xx2)`
= 28
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 he select a student if the monitor can be a boy or a girl?
Evaluate: 6!
Evaluate: (8 – 6)!
Compute: `(12!)/(6!)`
Compute: (3 × 2)!
Compute: 3! × 2!
Compute: `(8!)/(6! - 4!)`
Compute: `(8!)/((6 - 4)!)`
Write in terms of factorial:
5 × 6 × 7 × 8 × 9 × 10
Write in terms of factorial:
6 × 7 × 8 × 9
Find n, if `"n"/(8!) = 3/(6!) + 1/(4!)`
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!("n" - 3)!) : ("n"!)/(5!("n" - 5)!)` = 5:3
Find n, if: `((17 - "n")!)/((14 - "n")!)` = 5!
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!)`
A hall has 12 lamps and every lamp can be switched on independently. Find the number of ways of illuminating the hall.
