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what is the sum of all 3 digit numbers that can be formed using digits 0,1,2,3,4,5 without repetition
Read Solution (Total 8)
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- using this formula (n-1 )!* sum of digits*(11..n)
5*15*111=8325 - 6 years agoHelpfull: Yes(3) No(1)
- total no. of 3 digits numbers = 5*5*4=100
the sum of all numbers = 100*(0+1+2+3+4+5)*111= 166500 - 6 years agoHelpfull: Yes(2) No(2)
- by using formula -
(n-1)! * sum of all the digits * (number of ones depending on the number of digits specified)
here,
n=6
sum of all digits = 1+2+3+4+5 = 15
number of digits specified is 3, so we'll take 111
substituting,
(6-1)! * 15 * (111)
= 5! * 15 * 111
= 120 * 15 * 111
= 199800 - 6 years agoHelpfull: Yes(2) No(0)
- 120
6*5*4=120 - 6 years agoHelpfull: Yes(0) No(13)
- Total numbers using 5 given no.;
=>5*5*4=100; for 3 digit no.(o is not taken at 100 place i.e 1st place);
for one digit no.s sum using given 5 no.=(100/5)=20;
sum=>20*(0+1+2+3+4+5)*100=30000;
now for 10th digit place=20*15*10=3000;& 300
total=30000+3000+300=33300; - 6 years agoHelpfull: Yes(0) No(5)
- by using formula -
(n-1)! * sum of all the digits * (number of ones depending on the number of digits specified)
here,
n=6
sum of all digits = 1+2+3+4+5 = 15
number of digits specified is 3, so we'll take 111
substituting,
(6-1)! * 15 * (111)
= 5! * 15 * 111
= 120 * 15 * 111
= 199800
3 digit no. can not start with zero so
(1,2,3,4,5) sum of all the two digit words
(5-1)!*(1+2+3+4+5)*11=3960
now the sum is =199800-3960=195840 - 6 years agoHelpfull: Yes(0) No(0)
- 120
=>6*5*4=120 - 6 years agoHelpfull: Yes(0) No(0)
- We know that zero can't be in hundreds place. But let's assume that our number could start with zero.
The formula to find sum of all numbers in a permutation is
111 * no of ways numbers can be formed for a number at given position * sum of all given digits
No of 1 s depends on number of digits
So,the answer us
111 * 20 *(0+1+2+3+4+5) = 33300
We got 20 as follows..if we have 0 in units place we can form a number in 4*5 ways...this is for all numbers. So we have substituted 20 in formula..hope u understood
Now, this is not the final answer because we have included 0 in hundreds place...so we have to remove the sum of all numbers that starts with 0.
This is nothing but the sum of all 2 digits numbers formed by 1 2 3 4 5.. because 0 at first place makes it a 2 digit number.
So the sum for this is 11 * 4 * (1+2+3+4+5).
=660
Hope u understood why we use 4..each number can be formed in 4*1 ways
So, the final answer is 33300-660 = 32640 - 5 years agoHelpfull: Yes(0) No(0)
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