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प्रश्न
A hall has 12 lamps and every lamp can be switched on independently. Find the number of ways of illuminating the hall.
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उत्तर
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
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संबंधित प्रश्न
How many three-digit numbers can be formed using the digits 2, 3, 4, 5, 6 if digits can be repeated?
How many five-digit numbers formed using the digit 0, 1, 2, 3, 4, 5 are divisible by 3 if digits are not repeated?
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Compute: `(12!)/(6!)`
Compute: 3! × 2!
Compute: `(6! - 4!)/(4!)`
Write in terms of factorial:
3 × 6 × 9 × 12 × 15
Write in terms of factorial:
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Find n, if (n + 3)! = 110 × (n + 1)!
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Find n, if: `((17 - "n")!)/((14 - "n")!)` = 5!
Find the value of: `(8! + 5(4!))/(4! - 12)`
Show that: `((2"n")!)/("n"!)` = 2n(2n – 1)(2n – 3)....5.3.1
A question paper has 6 questions. How many ways does a student have if he wants to solve at least one question?
