@Yaman Sahu I realised this after publishing my comment. But could not delete because there are no such options.

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saykatamkeen
asked
in Analytical Aptitude
Sep 7, 2021

485 views
3 votes

$1$ million = $1000000$

so digits should be in the range of $1$ to $6$

for filling one digit we have $3$ options (either $0, 7, 8$)

so total possibility for $6$ digits $= 3^6 = 729$

out of which its count $000000 $ which is equal to $0,$ can’t be considered for this question.

so, total numbers $= 729 \ – 1 = 728$

**Note: **I am assuming numbers between $0$ and $1$ million in numbers greater than $0$ and less than $1$ million

@Yaman Sahu I realised this after publishing my comment. But could not delete because there are no such options.

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1 vote

**1 million = 1000000. **

**So, we have to consider up to 6 digit numbers. **

**For generalization, we consider all less than 6 digit numbers as six-digit numbers with ‘0’ as their beginning digit(s). **

**All six digits same: (3C1)*(6C6) = 3 **

**Five digits same: (3C1)*(2C1)*[(6!) / {(5!)*(1!)}] = 36 **

**Four digits same and remaining two digits using the others apiece: **

**(3C1)*(2C2)*[(6!) / {(4!)*(1!)*(1!)}] = 90**

**Four digits same and remaining two digits using the anyone from the remaining two twice: **

**(3C1)*(2C1)*[(6!) / {(4!)*(2!)}] = 180 **

**Three digits same and remaining three digits using anyone from the remaining two twice: **

**(3C1)*(2C1)*(1C1)*[(6!) / {(3!)*(2!)*(1!)}] = 360 **

**Using any two digits thrice each = (3C2)*[(6!) / {(3!)*(3!)}] = 60.**

**So, total ‘generalized’ 6-digit numbers can be formed using 0, 7 and 8 **

**= (3+36+90+180+360+60) **

**= 729. **

**But, these group of numbers include ‘000000’, which being equal to 0, can’t be considered for this question. **

**So, total numbers can be formed greater than 0 and less than a million using 0, 7 and 8 = 729 - 1 = 728.**

**Also, there is an easier method for this problem. **

**This time too, we’ve to consider ‘generalized’ 6-digit numbers. **

**Here for filling any particular digit’s place, we have 3 options. **

**So, total ‘generalized’ 6-digit numbers can be formed using 0, 7 and 8 = (3^6) = 729.**

**But, these group of ‘generalized’ 6-digit numbers include ‘000000’, which being equal to 0, can’t be considered for this question. **

**So, total numbers can be formed greater than 0 and less than a million using 0, 7 and 8 = 729 - 1 = 728....**