Advertisements
Advertisements
प्रश्न
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
Advertisements
उत्तर
The given numbers are 1, 2, 3, 4, 5
The total number of arrangements.
Using the digits 1, 2, 3, 4 and 5 taking 4 at a time is 5P4
= 5 × 4 × 3 × 2
= 120
∴ 120 four-digit numbers can be formed using the given 5 digits without repetition.
To find the sum of these numbers.
We will find the sum of digits at unit’s, ten’s, hundred’s and thousand’s place in all these 120 numbers.
Consider the digit in unit’s place. In all these numbers
Each of these digits 1, 2, 3, 4, 5 occurs 120 in `120/5`
= 24 times in the units place
∴ The sum of the digits at unit’s place
= 24(1 + 2 + 3 + 4 + 5)
= 24 × 15
= 360
Similarly sum of the digit’s at ten’s place = 360
Sum of the digit’s at hundred’s place = 360
Sum of the digit’s at thousand’s place = 360
∴ Sum of all four digit numbers formed using the digit’s 1, 2, 3, 4, 5
= 360 × 10° + 360 × 101 + 360 × 102 + 360 × 103
= 360(10° + 101 + 102 + 103)
= 360(1 + 10 + 100 + 1000)
= 360 × 1111
= 3,99,960
APPEARS IN
संबंधित प्रश्न
Evaluate 4! – 3!
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?
In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?
In how many ways can the letters of the word PERMUTATIONS be arranged if the vowels are all together.
In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?
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 ?
If three six faced die each marked with numbers 1 to 6 on six faces, are thrown find the total number of possible outcomes ?
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?
The number of arrangements of the word "DELHI" in which E precedes I is
Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is
The product of r consecutive positive integers is divisible by
Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?
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 even?
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
DANGER
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
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 ______.
8-digit numbers are formed using the digits 1, 1, 2, 2, 2, 3, 4, 4. The number of such numbers in which the odd digits do no occupy odd places is ______.
