wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The sum of all numbers greater than 1000 formed by using the digits 0,1,2,3, no digit being repeated in any number is

A
38664
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
48664
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
58664
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
None of these
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 38664
All the numbers are of 4 digits and they do not have 0 in thousand's place.
The number of numbers having 0 at unit's place=3! (as the other three places are to be filled by 1,2 or 3)
The number of numbers having 1 in unit's place=2P1×2P2 (as thousand's place can be filled by one of 2,3 and the remaining two places can be filled by the remaining two digits)
Similarly, the number of numbers having 2 or 3 in unit's place=2P1×2P2 in each case.
Thus the sum of digits in units place for all the numbers=3!×0+2P1×2P2×1+2P1×2P2×2+2P1×2P2×3=24
Similarly the sum of digits in ten's and hundredth's place=24 each.
Now thousand's place can be filled by 1,2 or 3.
Number of numbers having 1 in thousand's place=3! (as the other 3 places will be filled by 0,2,3)
Number of numbers having 2 or 3 in thousands place=3! each
Sum of digits in thousand's place for all the numbers=3!×1+3!×2+3!×3=36
Required sum of all numbers=36×1000+24×100+24×10+24×1=38664


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Why Do We Need to Manage Our Resources?
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon