A four digit number using the digits 3,4,6 and 7 without repetition

Question

A four digit number using the digits 3,4,6 and 7 without repetition is formed.All the possible numbers so formed are added and the sum is equal to P, which of the following is the value of P?

A.133200
B.123320
C.133220
D.133320
E.None of these.

Yogesh_24 · Accepted Answer

Here is a formula:
(n-1)!*(Sum of n digits)*(1111...n times)
Thus, in this case: n = 4, Sum of 4 digits = 20; therefore Total Sum = 3!*20*1111 which is equal to 133320

chetan2u · Answer

hi..
what will be the SUM of digits in each..
 in each position, each of 3,4,6,7 will stay for 3! ways...WHY? 
 say 3 is in units digit... how many such number are possible.. 
 thousands digit.. any of 3
humdreds digit.. any of remaining 2
tens digit remaining one
units digit.. digit 3 
so  3*2*1=3!=6 ..

so SUM is  6*(3+4+6+7)=120..

so number = 120*thousand+120*hundred+120*ten+120*one=120*1000+120*100+120*10+120*1=133320
D

gracie · Answer

least value=3,467
greatest value=7,643
3,467+7,643=11,110
11,110/2=5,555
4*6*5,555=133,320
D

DHAR · Answer

Hi  chetan2u : Can you please elaborate the highlighted part.Thank you

FB2017 · Answer

4*6*5,555=133,320
How do you come to the conclusion on the multiplication factors 4*6

malevg · Answer

Why? it is part of combinatorics. You have 3 digits (after one of 3,4, 6,7 is chosen) and all possible combinations for these digits in one number is 3!.

gracie · Answer

hi FB2017,
I put 3 in the first position and counted 6 possible arrangements for 4,6,7.
hence, 4*6
I hope this helps
gracie

pclawong · Answer

Dear Gracie,
I understand why you time 6 
but I don't understand why you time 4?
Thank you very much

Tpral · Answer

each number will be represented 6 times (for the unit, tenth , hundred etc..)

Sum of unit Digit: 6 (7+6+4+3)=120
Sum of tenth Digit: 6 (7+6+4+3)=120
Sum of hundred Digit: 6 (7+6+4+3)=120
...

.. 120 000
+.. 120 00
+.... 120 0
+...... 120 
---------
...133320

gracie · Answer

hi pclawong,
I multiplied by 4 because there are 4 digits, 
each giving 6 possible arrangements of the other 3
I hope this helps
gracie

aspreneur · Answer

hey gracie, why did you divide 11110/2?

gracie · Answer

hi aspreneur,

to find the arithmetic mean of the the lowest and highest value combinations,
to multiply it by the number of possible combinations
I hope this helps
gracie

CAMANISHPARMAR · Answer

Total possible numbers are 4!=24
Each of the 4 digits repeat 6 times in units, tens, hundreds and thousands place:- 
(3333 + 4444 + 6666 + 7777) * 6

= 1111 (3 + 4 + 6 + 7) * 6

= 1111 (20) * 6

= 22220 * 6

= 133320 (Ans D)

CAMANISHPARMAR · Answer

Here is the derivation of the formula:-
Total possible numbers are 4!=24
Each of the 4 digits repeat 6 times in units, tens, hundreds and thousands place:-
(3333 + 4444 + 6666 + 7777) * 6

= 1111 * (3 + 4 + 6 + 7) * 6

= 1111 * (20) * 6

= 22220 * 6

= 133320 (Ans D)

SSM700plus · Answer

If all possible n digit numbers using n distinct non-zero digits are formed, sum of all the numbers so formed
=(n−1)! × (sum of the all the digits in numbers ) × (111 ... n times).

It is a 4 digit number . n =4

Just substitute the value.
= (4-1)! * (3+4+6+7) * (1111)
= 3! * 20 * 1111
= 6*20*1111
= 133320.

Answer D

firas92 · Answer

Number of 4 digit numbers that can be formed using the digits 3,4,6,7 is 4!=24

Now every number will have a corresponding pair such that the sum of digits in each position is 10 (for example 3467,7643), the sum of which will be 11110.

12 such pairs are possible

So required sum is 11110*12=133320

Answer is  (D)

Hit Kudos if this helped!

Posted from my mobile device

Arssalan8 · Answer

The simplest way to solve this question is to do it in 3 steps.

Step 1: we calculate the possible numbers ie 4*3*2*1= 24 numbers are possible without repetition.

Step 2: we calculate the mean as follows 
3,467+7,643 / 2 = 5,555

Step 3= multiply the mean with the number of digits and will come as D

Posted from my mobile device

bumpbot · Answer

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A four digit number using the digits 3,4,6 and 7 without repetition

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