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
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
Compute `(8!)/(6! xx 2!)`
How many 4-digit numbers are there with no digit repeated?
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?
Find r if `""^5P_r = 2^6 P_(r-1)`
In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?
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 ASSASSINATION be arranged so that all the S’s are together?
Which of the following are true:
(2 × 3)! = 2! × 3!
How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
How many numbers of six digits can be formed from the digits 0, 1, 3, 5, 7 and 9 when no digit is repeated? How many of them are divisible by 10 ?
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?
In how many ways can 7 letters be posted in 4 letter boxes?
Evaluate each of the following:
6P6
Write the number of 5 digit numbers that can be formed using digits 0, 1 and 2 ?
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 different signals which can be given from 6 flags of different colours taking one or more at a time, 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
If k + 5Pk + 1 =\[\frac{11 (k - 1)}{2}\]. k + 3Pk , then the values of k are
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
English alphabet has 11 symmetric letters that appear same when looked at in a mirror. These letters are A, H, I, M, O, T, U, V, W, X and Y. How many symmetric three letters passwords can be formed using these letters?
How many five digits telephone numbers can be constructed using the digits 0 to 9 If each number starts with 67 with no digit appears more than once?
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:
If n is a positive integer, then the number of terms in the expansion of (x + a)n is:
The number of ways to arrange the letters of the word “CHEESE”:
The number of words with or without meaning that can be formed using letters of the word “EQUATION”, with no repetition of letters is:
The number of permutation of n different things taken r at a time, when the repetition is allowed is:
Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?
8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?
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
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
The number of 5-digit telephone numbers having atleast one of their digits repeated 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`.
If 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.
