Advertisements
Advertisements
Question
A hall has 12 lamps and every lamp can be switched on independently. Find the number of ways of illuminating the hall.
Advertisements
Solution
Every lamp is either ON or OFF.
There are 12 lamps
Number of instances = 212
This number includes the case in which all 12
lamps are OFF.
∴ Required Number = 212 – 1 = 4095
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?
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?
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!
Evaluate: (8 – 6)!
Compute: `(12/6)!`
Compute: `(9!)/(3! 6!)`
Write in terms of factorial:
5 × 6 × 7 × 8 × 9 × 10
Find n, if `"n"/(8!) = 3/(6!) + 1/(4!)`
Find n if: `("n"!)/(3!("n" - 3)!) : ("n"!)/(5!("n" - 5)!)` = 5:3
Find n if: `("n"!)/(3!("n" - 5)!) : ("n"!)/(5!("n" - 7)!)` = 10:3
Find n, if: `((17 - "n")!)/((14 - "n")!)` = 5!
Find n, if: `((2"n")!)/(7!(2"n" - 7)!) : ("n"!)/(4!("n" - 4)!)` = 24:1
Show that: `(9!)/(3!6!) + (9!)/(4!5!) = (10!)/(4!6!)`
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 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.
