Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
In order to get the 6-digit number divisible by 4
The last two digits must be divisible by 4
∴ The last two digits should be 12 or 24 or 32
| 24 | ||||
| 1 | 2 | 3 | 4 | 5 |
Let the last box be filled with 24.
The remaining 4 boxes can be filled with the remaining digits
1, 1, 3, 3 in `(4!)/(2! xx 2!)` ways.
| 12 | ||||
| 1 | 2 | 3 | 4 | 5 |
Let the last box be filled with 12.
The remaining 4 boxes can be filled with the remaining digits.
1, 3, 3, 4 in `(4!)/(2!)` ways
| 32 | ||||
| 1 | 2 | 3 | 4 | 5 |
Let the last box be filled with 32.
The remaining 4 boxes can be filled with the remaining digits
The total number of 6 digit numbers which are divisible by 4 is
= `(4!)/(2! xx 2!) + (4!)/(2!) + (4!)/(2!)`
= `(1 xx 2 xx 3 xx 4)/(1 xx 2 xx 1 xx 2) + (1 xx 2 xx 3 xx 4)/(1 xx 2) + (1 xx 2 xx 3 xx 4)/(1 xx 2)`
= 6 + 12 + 12
= 30
∴ Required number of 6-digit numbers = 30
APPEARS IN
संबंधित प्रश्न
Evaluate 8!
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 = ""^6P_(r-1)`
Find the number of ways in which 8 distinct toys can be distributed among 5 childrens.
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 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
The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is
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
The number of words that can be made by re-arranging the letters of the word APURBA so that vowels and consonants are alternate is
If (n+2)! = 60[(n–1)!], find n
Evaluate the following.
`(3! + 1!)/(2^2!)`
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?
How many strings are there using the letters of the word INTERMEDIATE, if all the vowels 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 never together.
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)`
If 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.
