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
if `1/(6!) + 1/(7!) = x/(8!)`, find x
Find n if n – 1P3 : nP4 = 1 : 9
In how many ways can the letters of the word PERMUTATIONS be arranged if the vowels are all together.
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?
How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
Find the number of ways in which one can post 5 letters in 7 letter boxes ?
Write the number of all possible words that can be formed using the letters of the word 'MATHEMATICS'.
Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is
If the letters of the word KRISNA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word KRISNA is
The product of r consecutive positive integers is divisible by
- In how many ways can 8 identical beads be strung on a necklace?
- In how many ways can 8 boys form a ring?
Find the rank of the word ‘CHAT’ in the dictionary.
8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?
8 women and 6 men are standing in a line. In how many arrangements will all 6 men be standing next to one another?
Find the distinct permutations of the letters of the word MISSISSIPPI?
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)`
Ten different letters of alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated is ______.
Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together
The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is ______.
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.
