Advertisements
Advertisements
प्रश्न
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 ?
Advertisements
उत्तर
The first digit of the number cannot be zero. Thus, it can be filled in 5 ways.
The number of ways of filling the second digit = 5
(as the repetition of digits is not allowed)
The number of ways of filling the third digit = 4
The number of ways of filling the fourth digit = 3
The number of ways of filling the fifth digit = 2
The number of ways of filling the sixth digit = 1
∴ Required numbers =`5xx5xx4xx3xx2xx1=600`
For the number to be divisible by 10, the sixth digit has to be zero.
Now, the first digit can be filled in 5 ways.
Number of ways of filling the second digit = 4
Number of ways of filling the third digit = 3
Number of ways of filling the fourth digit = 2
Number of ways of filling the fifth digit = 1
Number of ways of filling the sixth digit = 1
Total numbers divisible by 10 =`5xx4xx3xx2xx1xx1=120`
APPEARS IN
संबंधित प्रश्न
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
Find n if n – 1P3 : nP4 = 1 : 9
Find r if `""^5P_r = 2^6 P_(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?
In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?
Find x in each of the following:
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.
Find the number of ways in which one can post 5 letters in 7 letter boxes ?
Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?
Evaluate each of the following:
P(6, 4)
In how many ways 4 women draw water from 4 taps, if no tap remains unused?
Write the number of arrangements of the letters of the word BANANA in which two N's come together.
Write the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together ?
Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?
The number of words that can be formed out of the letters of the word "ARTICLE" so that vowels occupy even places is
How many numbers greater than 10 lacs be formed from 2, 3, 0, 3, 4, 2, 3 ?
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
The number of ways to arrange the letters of the word CHEESE are
If k + 5Pk + 1 =\[\frac{11 (k - 1)}{2}\]. k + 3Pk , then the values of k are
The number of arrangements of the letters of the word BHARAT taking 3 at a time is
If (n+2)! = 60[(n–1)!], find n
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”.
If `""^(("n" – 1))"P"_3 : ""^"n""P"_4` = 1 : 10 find n
Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?
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.
What is the maximum number of different answers can the students give?
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
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 divisible by 4?
Choose the correct alternative:
If `""^(("n" + 5))"P"_(("n" + 1)) = ((11("n" - 1))/2)^(("n" + 3))"P"_"n"`, then the value of n are
In how many ways can 5 children be arranged in a line such that two particular children of them are never together.
If all permutations of the letters of the word AGAIN are arranged in the order as in a dictionary. What is the 49th word?
Suppose m men and n women are to be seated in a row so that no two women sit together. If m > n, show that the number of ways in which they can be seated is `(m!(m + 1)!)/((m - n + 1)1)`
Find the number of permutations of n different things taken r at a time such that two specific things occur together.
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 |
