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
if `1/(6!) + 1/(7!) = x/(8!)`, find x
Evaluate `(n!)/((n-r)!)`, when n = 9, r = 5
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)`
If three six faced die each marked with numbers 1 to 6 on six faces, are thrown find the total number of possible outcomes ?
Evaluate each of the following:
P(6, 4)
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 product of r consecutive positive integers is divisible by
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 5 and r = 2.
How many five digits telephone numbers can be constructed using the digits 0 to 9 If each number starts with 67 with no digit appears more than once?
- In how many ways can 8 identical beads be strung on a necklace?
- In how many ways can 8 boys form a ring?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if the first four questions have three choices and the remaining have five choices?
In how many ways 4 mathematics books, 3 physics books, 2 chemistry books and 1 biology book can be arranged on a shelf so that all books of the same subjects are together
A coin is tossed 8 times, how many different sequences containing six heads and two tails are possible?
How many strings are there using the letters of the word INTERMEDIATE, if no two vowels 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?
The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently is ______.
In how many ways 3 mathematics books, 4 history books, 3 chemistry books and 2 biology books can be arranged on a shelf so that all books of the same subjects are together.
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 ______.
If m+nP2 = 90 and m–nP2 = 30, then (m, n) is given by ______.
