Advertisements
Advertisements
Question
Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is
Options
24
30
125
100
Advertisements
Solution
24
In order to make a number divisible by 4, its last two digits must be divisible by 4, which in this case can be 12, 24, 32 or 52.
Since repetition of digits is not allowed, the remaining first two digits can be arranged in 3 x 2 ways in each case.
∴ Total number of numbers that can be formed = 4 x {3 x 2} = 24
APPEARS IN
RELATED QUESTIONS
Evaluate `(n!)/((n-r)!)` when n = 6, r = 2
From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?
Which of the following are true:
(2 +3)! = 2! + 3!
Which of the following are true:
(2 × 3)! = 2! × 3!
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.
In how many ways can 4 prizes be distributed among 5 students, when
(i) no student gets more than one prize?
(ii) a student may get any number of prizes?
(iii) no student gets all the prizes?
Evaluate each of the following:
6P6
Write the number of 5 digit numbers that can be formed using digits 0, 1 and 2 ?
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 words that can be formed out of the letters of the word 'COMMITTEE' ?
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 ?
Write the number of numbers that can be formed using all for digits 1, 2, 3, 4 ?
The number of five-digit telephone numbers having at least one of their digits repeated is
The number of ways in which the letters of the word 'CONSTANT' can be arranged without changing the relative positions of the vowels and consonants is
The number of different ways in which 8 persons can stand in a row so that between two particular persons A and B there are always two persons, is
In a room there are 12 bulbs of the same wattage, each having a separate switch. The number of ways to light the room with different amounts of illumination is
Find x if `1/(6!) + 1/(7!) = x/(8!)`
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 5 and r = 2.
In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?
Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.
The possible outcomes when a coin is tossed five times:
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?
If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then find the ranks of the words
DANGER
Find the number of strings that can be made using all letters of the word THING. If these words are written as in a dictionary, what will be the 85th string?
If all permutations of the letters of the word AGAIN are arranged in the order as in a dictionary. What is the 49th word?
Ten different letters of alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated is ______.
The number of signals that can be sent by 6 flags of different colours taking one or more at a time is ______.
The total number of 9 digit numbers which have all different digits is ______.
The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.
In the permutations of n things, r taken together, the number of permutations in which m particular things occur together is `""^(n - m)"P"_(r - m) xx ""^r"P"_m`.
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 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.
The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.
