how many six digit number can be formed using all the digits 1,2,3,0,7,9? solution the sum answer please
Answers
Answered by
1
Answer:
36. 6*6=36. please go ahead and check. like
Answered by
6
Answer:
Complete step-by-step answer:
First of all, write the divisibility rule of 11.
Let the digit is written as abcdef, then, the digit is divisible by 11 if and if (a+c+e)−(b+d+f) is 0 or a multiple of 11.
We have possible that a,b,c,d,e,f can take to satisfy the divisibility of 11.
If each of a,c,e can take any value from 7,5,0. Then b,d,f can take 9,2 or 1.
But, a cannot take 0 as it will make a five-digit number then.
a has 2 options, c
has 2 options, if any of them is taken by a and e
will be left with only 1 option.
Similarly, b can take 3 options, d has 2 options and f has one option left.
Total cases are for abcdef when a,c,e can take any value from 7,5,0 and b,d,f can take 9,2 or 1are 2×3×2×2×1×1=24
Similarly take the case when b,d,f can take any value from 7,5,0 and a,c,e can take 9,2 or1.
b can take 3 options, d has 2 options and f has one option left
And similarly a can take 3 options, c
has 2 options and e
has one option left.
Hence, total number of ways for this case is 3×3×2×2×1×1=36
Therefore, the number of 6 digit numbers that can be formed using the digits 0,1,2,5,7 and 9 which are divisible by 11 and no digit is repeated is sum of 24 and 36, which is 60.
Hence, option 2 is correct.
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