Advertisements
Advertisements
प्रश्न
A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is
विकल्प
216
600
240
3125
Advertisements
उत्तर
216
A number is divisible by 3 when the sum of the digits of the number is divisible by 3.
Out of the given 6 digits, there are only two groups consisting of 5 digits whose sum is divisible by 3.
1+2+3+4+5 = 15
0+1+2+4+5 = 12
Using the digits 1, 2, 3, 4 and 5, the 5 digit numbers that can be formed = 5!
Similarly, using the digits 0, 1, 2, 4 and 5, the number that can be formed = 5! - 4! {since the first digit cannot be 0}
∴ Total numbers that are possible = 5! + 5! - 4! = 240 -24 = 216
APPEARS IN
संबंधित प्रश्न
Compute `(8!)/(6! xx 2!)`
if `1/(6!) + 1/(7!) = x/(8!)`, find x
Find r if `""^5P_r = 2^6 P_(r-1)`
Find r if `""^5P_r = ""^6P_(r-1)`
How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?
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 three jobs I, II and III be assigned to three persons A, B and C if one person is assigned only one job and all are capable of doing each job?
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?
Write the number of arrangements of the letters of the word BANANA in which two N's come together.
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 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
The number of six letter words that can be formed using the letters of the word "ASSIST" in which S's alternate with other letters is
Find x if `1/(6!) + 1/(7!) = x/(8!)`
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! + 1!)/(2^2!)`
The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for all n ∈ N is:
How many strings can be formed from the letters of the word ARTICLE, so that vowels occupy the even places?
8 women and 6 men are standing in a line. In how many arrangements will all 6 men be standing next to one another?
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 vowels are never together
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
GARDEN
If the letters of the word FUNNY are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, find the rank of the word FUNNY
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
Choose the correct alternative:
If `""^(("n" + 5))"P"_(("n" + 1)) = ((11("n" - 1))/2)^(("n" + 3))"P"_"n"`, then the value of n are
The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently is ______.
If all permutations of the letters of the word AGAIN are arranged in the order as in a dictionary. What is the 49th word?
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.
The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.
Five boys and five girls form a line. Find the number of ways of making the seating arrangement under the following condition:
| C1 | C2 |
| (a) Boys and girls alternate: | (i) 5! × 6! |
| (b) No two girls sit together : | (ii) 10! – 5! 6! |
| (c) All the girls sit together | (iii) (5!)2 + (5!)2 |
| (d) All the girls are never together : | (iv) 2! 5! 5! |
How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
| C1 | C2 |
| (a) 4 letters are used at a time | (i) 720 |
| (b) All letters are used at a time | (ii) 240 |
| (c) All letters are used but the first is a vowel | (iii) 360 |
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 ______.
The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.
Number of words from the letters of the words BHARAT in which B and H will never come together is ______.
