Advertisements
Advertisements
प्रश्न
A five-digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5 without repetitions. The total number of ways this can be done is ______.
पर्याय
216
600
240
3125
उत्तर
A five-digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5 without repetitions. The total number of ways this can be done is 216.
Explanation:
We know that a number is divisible by 3 when the sum of its digits is divisible by 3.
If we take the digits 0, 1, 2, 4, 5, then the sum of the digits
= 0 + 1 + 2 + 4 + 5 = 12 which is divisible by 3
So, the 5 digit numbers using the digits 0, 1, 2, 4, and 5
TTh Th H T O
4 4 3 2 1
= 4 × 4 × 3 × 2 × 1
= 96
And if we take the digits 1, 2, 3, 4, 5, then their sum
= 1 + 2 + 3 + 4 + 5
= 15 divisible by 3
So, five-digit numbers can be formed using the digits 1, 2, 3, 4, 5 is 5! ways
= 5 × 4 × 3 × 2 × 1
= 120 ways
Total number of ways = 96 + 120
= 216.
APPEARS IN
संबंधित प्रश्न
Compute `(8!)/(6! xx 2!)`
if `1/(6!) + 1/(7!) = x/(8!)`, find x
Evaluate `(n!)/((n-r)!)` when n = 6, r = 2
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 x in each of the following:
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?
In how many ways can 7 letters be posted in 4 letter boxes?
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 all possible words that can be formed using the letters of the word 'MATHEMATICS'.
The number of words that can be formed out of the letters of the word "ARTICLE" so that vowels occupy even places is
The number of words from the letters of the word 'BHARAT' in which B and H will never come together, 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 numbers lesser than 1000 can be formed using the digits 5, 6, 7, 8, and 9 if no digit is repeated?
Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.
The number of ways to arrange the letters of the word “CHEESE”:
A test consists of 10 multiple choice questions. In how many ways can the test be answered if the first four questions have three choices and the remaining have five choices?
A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.
How will the answer change if each question may have more than one correct answers?
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
How many strings are there using the letters of the word INTERMEDIATE, if no two vowels are together
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
In how many ways can 5 children be arranged in a line such that two particular children of them are always together
In how many ways can 5 children be arranged in a line such that two particular children of them are never together.
There are 10 persons named P1, P2, P3, ... P10. Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.
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 |
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.
