Advertisements
Advertisements
Question
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
Advertisements
Solution
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
RELATED QUESTIONS
Is 3! + 4! = 7!?
Evaluate `(n!)/((n-r)!)` when n = 6, r = 2
Find r if `""^5P_r = 2^6 P_(r-1)`
A coin is tossed three times and the outcomes are recorded. How many possible outcomes are there? How many possible outcomes if the coin is tossed four times? Five times? n times?
Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?
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 ?
The number of five-digit telephone numbers having at least one of their digits repeated is
The number of six letter words that can be formed using the letters of the word "ASSIST" in which S's alternate with other letters is
The number of arrangements of the letters of the word BHARAT taking 3 at a time is
In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?
- In how many ways can 8 identical beads be strung on a necklace?
- In how many ways can 8 boys form a ring?
Evaluate the following.
`(3! xx 0! + 0!)/(2!)`
In how many ways can the letters of the word SUCCESS be arranged so that all Ss 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?
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
If the letters of the word FUNNY are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, find the rank of the word FUNNY
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. How many telephone numbers have all six digits distinct?
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 |
The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is ______.
