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
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 girl or a boy?
How many two letter words can be formed using letters from the word SPACE, when repetition of letters is not allowed?
How many three-digit numbers can be formed from the digits 0, 1, 3, 5, 6 if repetitions of digits are allowed?
How many three-digit numbers can be formed using the digits 2, 3, 4, 5, 6 if digits can be repeated?
In a test, 5 questions are of the form 'state, true or false'. No student has got all answers correct. Also, the answer of every student is different. Find the number of students appeared for the test.
How many numbers between 100 and 1000 have the digit 7 exactly once?
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
There are 3 types of toy car and 2 types of toy train available in a shop. Find the number of ways a baby can buy a toy car and a toy train?
Count the number of three-digit numbers which can be formed from the digits 2, 4, 6, 8 if repetitions of digits is not allowed
To travel from a place A to place B, there are two different bus routes B1, B2, two different train routes T1, T2 and one air route A1. From place B to place C there is one bus route say B1, two different train routes say T1, T2 and one air route A1. Find the number of routes of commuting from place A to place C via place B without using similar mode of transportation
How many strings can be formed using the letters of the word LOTUS if the word either starts with L or ends with S?
Count the total number of ways of answering 6 objective type questions, each question having 4 choices
Find the value of 6!
Find the value of 3! × 2!
Find the value of `(12!)/(9! xx 3!)`
Find the value of `(("n" + 3)!)/(("n" + 1)!)`
Find the value of n if `1/(8!) + 1/(9!) = "n"/(10!)`
Choose the correct alternative:
The sum of the digits at the 10th place of all numbers formed with the help of 2, 4, 5, 7 taken all at a time is
The number of ways in which a garland can be formed by using 10 identical pink flowers and 9 identical white flowers is ______
All the letters of the word PADMAPRIYA are placed at random in a row. The probability that the word PRIY A occurs without getting split is ______
How many numbers are there between 99 and 1000 having 7 in the units place?
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 ______.
A candidate is required to answer 7 questions out of 12 questions, which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. Find the number of different ways of doing question
Out of 18 points in a plane, no three are in the same line except five points which are collinear. Find the number of lines that can be formed joining the point
Find the number of positive integers greater than 6000 and less than 7000 which are divisible by 5, provided that no digit is to be repeated.
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 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 ______.
The number of six-digit numbers, all digits of which are odd is ______.
In a steamer there are stalls for 12 animals, and there are horses, cows and calves (not less than 12 each) ready to be shipped. They can be loaded in 312 ways.
There will be only 24 selections containing at least one red ball out of a bag containing 4 red and 5 black balls. It is being given that the balls of the same colour are identical.
If the number of five-digit numbers with distinct digits and 2 at the 10th place is 336 k, then k is equal to ______.
