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# The sum of all 4 digit number containing the digits 2, 4, 6, 8, without repetitions isa)133330b)122220c)213330d)133320Correct answer is 'D'. Can you explain this answer? Related Test: Test: Basic Concepts Of Permutations And Combinations- 1

## CA Foundation Question

 Sandhya Grewal May 28, 2018
As the 2,4,6,8 creates Arithmetic progression (A.P.)
THE FORMULA FOR THIS is:

n!/2(first term +last term)

Using 2,4,6,8: smallest number will be 2468 and this will be first number and 8642 will be the last and largest number.

so,
the value of n! is 4!=24
as 4 numbers can be arranged on 4! ways without repetition=24

Hence,
24/2 (2,468+8,642)
=12(11,110)
=133320

 Be Positive Sep 08, 2020
Upar diye gye prashn ka sabse aasaan trika
pehle to samjhte hain ki prashn kehna kya chahta hain
usme (2,4,6,8) 4 alag alag anukramank diye gye hain uske jitne sankhya ban skte hain banana hai phir sabko jod dena hain...,
1111 x (2+4+6+8) x 4!/4 ----> ye aapka aasan trika hain
1111 ye kramank honge utne hi digit lene hain
(2+4+6+8) ye sabka sum hai yaani diye gye 4 kramank ko jod dijiye
4!/4 kitne no. ki possibility hain usse n se divide kr dijiye

1111 x 20 x 6
1,33,320

=4!/4(20)(1111)
=24/4(20)(1111)
=6(20)(1111)
=133320

 Shubhangi Singhal Oct 19, 2019
(2+4+6+8) ×3! ×1111 =133320

 Nandita Shekhar Nov 16, 2020
(n-1)! (sum of all digits) (111..... n times)

3! (2+4+6+8) (1111)

6×20*1111

ans :133320

 Udita Kaushik Kaushik Mar 12, 2021
Step 1= 4×3×2×1=24
step 2= 24/4=6
step 3= 2+4+6+8=20
step 4= step 2 ×step 3=6×20=120
step 5= 120×1000+120×100+120×10+120×1=133320

 Ananth Anantham Mar 11, 2021
D option
2,4,6,8 =4!
24/2=12
2468+8642=12(11110)=133320

 Sakshi Pardeshi 3 weeks ago
Requirement is sum of 4 digit number
so, 4!=24
containing 4 digits hence 24/4 =6
6*(2+4+6+8)=120....this is sum of first digit
so we can do this in following way
120
120*10=1200
120*100=12000
120*1000=120000
summation of all
120+1200+12000+120000=133320
hence proved

 Archa T.a Dec 01, 2020
Take the sum of all numbers i e, 2+4+6+8=20.
take the average of the sum and it gives =20/4 =5
then, take the average of the sum that is 5 as the 4 digit number then the 4 digit number =5555
and multiply it with 4! that is 4*3*2*1=24.
and then we get 5555*24 which is =133320(option(d))

 Only Status Apr 07, 2021
1) 4!=24.

2)24/4=6.

3) 2*6=12.
+4*6=24.
+6*6=36.
+8*6=48.
_____
120
4)120
+1200
+12000
+120000=133320.

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