Advertisements
Advertisements
Question
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated ?
Advertisements
Solution
Total number of lamps = 10
A lamp can be either switched on or switched off.
Since, at least one lamp is to be kept switched on,
∴ The total number of ways are `2^10-1=1023`
Thus, the number of ways in which the hall can be illuminated are 1023.
APPEARS IN
RELATED QUESTIONS
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
How many 4-digit numbers are there with no digit repeated?
Find r if `""^5P_r = 2^6 P_(r-1)`
In how many ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S.
In how many ways can the letters of the word PERMUTATIONS be arranged if the vowels are all together.
Find x in each of the following:
A customer forgets a four-digits code for an Automatic Teller Machine (ATM) in a bank. However, he remembers that this code consists of digits 3, 5, 6 and 9. Find the largest possible number of trials necessary to obtain the correct code.
How many numbers of four digits can be formed with the digits 1, 2, 3, 4, 5 if the digits can be repeated in the same number?
How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?
How many 5-digit telephone numbers can be constructed using the digits 0 to 9. If each number starts with 67 and no digit appears more than once?
Evaluate each of the following:
6P6
In how many ways 4 women draw water from 4 taps, if no tap remains unused?
Write the total number of possible outcomes in a throw of 3 dice in which at least one of the dice shows an even number.
Write the number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys ?
The number of permutations of n different things taking r at a time when 3 particular things are to be included is
The number of different signals which can be given from 6 flags of different colours taking one or more at a time, is
How many numbers lesser than 1000 can be formed using the digits 5, 6, 7, 8, and 9 if no digit is repeated?
In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?
Find the rank of the word ‘CHAT’ in the dictionary.
Evaluate the following.
`((3!)! xx 2!)/(5!)`
The possible outcomes when a coin is tossed five times:
If `""^(("n" – 1))"P"_3 : ""^"n""P"_4` = 1 : 10 find n
8 women and 6 men are standing in a line. In how many arrangements will no two men be standing next to one another?
In how many ways 4 mathematics books, 3 physics books, 2 chemistry books and 1 biology book can be arranged on a shelf so that all books of the same subjects are together
A coin is tossed 8 times, how many different sequences of heads and tails are possible?
How many strings are there using the letters of the word INTERMEDIATE, if all the vowels are together
How many strings are there using the letters of the word INTERMEDIATE, if no two vowels are together
Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many of these 6-digit numbers are even?
Choose the correct alternative:
The product of r consecutive positive integers is divisible b
The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently is ______.
Using the digits 1, 2, 3, 4, 5, 6, 7, a number of 4 different digits is formed. Find
| C1 | C2 |
| (a) How many numbers are formed? | (i) 840 |
| (b) How many number are exactly divisible by 2? | (i) 200 |
| (c) How many numbers are exactly divisible by 25? | (iii) 360 |
| (d) How many of these are exactly divisible by 4? | (iv) 40 |
Let b1, b2, b3, b4 be a 4-element permutation with bi ∈ {1, 2, 3, .......,100} for 1 ≤ i ≤ 4 and bi ≠ bj for i ≠ j, such that either b1, b2, b3 are consecutive integers or b2, b3, b4 are consecutive integers. Then the number of such permutations b1, b2, b3, b4 is equal to ______.
If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is ______.
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Determine the number of words which have at least one letter repeated.
8-digit numbers are formed using the digits 1, 1, 2, 2, 2, 3, 4, 4. The number of such numbers in which the odd digits do no occupy odd places is ______.
