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
Is 3! + 4! = 7!?
Evaluate `(n!)/((n-r)!)` when n = 6, r = 2
Find x in each of the following:
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 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 ?
Write the number of ways in which 7 men and 7 women can sit on a round table such that no two women sit together ?
Write the number of words that can be formed out of the letters of the word 'COMMITTEE' ?
The number of words from the letters of the word 'BHARAT' in which B and H will never come together, is
The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is
Find x if `1/(6!) + 1/(7!) = x/(8!)`
The number of permutation of n different things taken r at a time, when the repetition is allowed is:
If `""^(("n" – 1))"P"_3 : ""^"n""P"_4` = 1 : 10 find n
A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.
How will the answer change if each question may have more than one correct answers?
How many ways can the product a2 b3 c4 be expressed without exponents?
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 distinct 6-digit numbers are there?
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?
The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.
In the permutations of n things, r taken together, the number of permutations in which m particular things occur together is `""^(n - m)"P"_(r - m) xx ""^r"P"_m`.
If 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.
