Advertisements
Advertisements
प्रश्न
Answer the following:
A hall has 12 lamps and every lamp can be switched on independently. Find the number of ways of illuminating the hall.
Advertisements
उत्तर
There are 12 lamps, i.e., n = 12.
Now, if at least one of the switches is 'on' the hall can be illuminated.
∴ the number of ways in which the hall can be illuminated = 2n – 1
= 212 – 1
= 4096 – 1
= 4095
APPEARS IN
संबंधित प्रश्न
How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is not allowed?
Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?
How many numbers between 100 and 1000 have 4 in the units place?
How many two letter words can be formed using letters from the word SPACE, when repetition of letters is allowed?
How many three-digit numbers can be formed from the digits 0, 1, 3, 5, 6 if repetitions of digits are not allowed?
How many numbers between 100 and 1000 have 4 in the units place?
How many numbers between 100 and 1000 have the digit 7 exactly once?
If numbers are formed using digits 2, 3, 4, 5, 6 without repetition, how many of them will exceed 400?
How many numbers formed with the digits 0, 1, 2, 5, 7, 8 will fall between 13 and 1000 if digits can be repeated?
Select the correct answer from the given alternatives.
A college offers 5 courses in the morning and 3 in the evening. The number of ways a student can select exactly one course, either in the morning or in the evening
How many words can be formed by writing letters in the word CROWN in different order?
How many two-digit numbers can be formed using 1, 2, 3, 4, 5 without repetition of digits?
In how many ways 5 persons can be seated in a row?
Given four flags of different colours, how many different signals can be generated if each signal requires the use of three flags, one below the other?
How many numbers are there between 100 and 500 with the digits 0, 1, 2, 3, 4, 5? if repetition of digits allowed
How many numbers are there between 100 and 500 with the digits 0, 1, 2, 3, 4, 5? if the repetition of digits is not allowed
Count the numbers between 999 and 10000 subject to the condition that there are no digit is repeated
Count the numbers between 999 and 10000 subject to the condition that there are at least one of the digits is repeated
How many three-digit numbers, which are divisible by 5, can be formed using the digits 0, 1, 2, 3, 4, 5 if repetition of digits are not allowed?
In how many ways 10 pigeons can be placed in 3 different pigeon holes?
Find the value of 6!
Find the value of 4! + 5!
Find the value of `(("n" + 3)!)/(("n" + 1)!)`
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 6, r = 2
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 10, r = 3
Evaluate `("n"!)/("r"!("n" - "r")!)` when for any n with r = 2
Choose the correct alternative:
There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two points is
In how many ways can this diagram be coloured subject to the following two conditions?
(i) Each of the smaller triangle is to be painted with one of three colours: red, blue or green.
(ii) No two adjacent regions have the same colour.
In an examination there are three multiple choice questions and each question has 4 choices. Number of ways in which a student can fail to get all answer correct is ______.
Find the number of integers greater than 7000 that can be formed with the digits 3, 5, 7, 8 and 9 where no digits are repeated.
The number of possible outcomes when a coin is tossed 6 times is ______.
The sum of the digits in unit place of all the numbers formed with the help of 3, 4, 5 and 6 taken all at a time is ______.
If the number of five-digit numbers with distinct digits and 2 at the 10th place is 336 k, then k is equal to ______.
