Question

How many 3-digit numbers can be formed using only the digits 1 to 7 if the number 2 must be included. Repetition is allowed

Answer 1

possibility
2**
*2*
**2

so it would be 3*7*7 (2 can be repeated as well, right ?)

Answer 2

1st find total 3 digits numbers which can be formed by using numbers from the set -> [1-7]

then subtract the number of 3 digit numbers which don't have a single 2 in them and have digits only from this set-> [1-7]-{2}

Answer 3

Thats a very lengthy way to go about things. I bet there is a cleaner solution

Answer 4

think of it as this:-
there is 3 ways to arrange a number 2 as fixed in 3-digit number right ?
then found the how many 2-digits number can be formed from 1 to 7.
just like that :3

Answer 5

Ok So I came up with 7^3-6^3=127

Answer 6

Thanks guys ....
I was thinking of manually going through all the numbers that dont include 2 and i was like hmmm that wld be lengthy
And then I came back to the problem and Eureka .... im like we can cut to the chase by just subtracting 6^3