Question

How many numbers can you form using the digits 2, 3, 4, 6, 5,1,0 if the digits formed are numbers less than 100 with non repeating digits?

Answer 1

43

Explanation:

Think intuitively. There're 7 digits. we want to form numbers that are less than 100. To do so it, figure out the permutation of 2 out of 7. Mathematically

`P(7,2)=(7!)/((7-2)!)`

And it simplifies to 42. Note that for simplicity, we're considering two digits numbers with 0 in the ten digit place as a single number for instance, two digits number like 04 are being considered 4 only etc. So are we done? No, we of course have to include 0 which is less than 100. Hence the answer is 42+1=43. Therefore 43 numbers can be formed using the digits 2, 3, 4, 6, 5,1,0 if the digits formed are numbers less than 100 with non repeating digits

(and forget whatever I said in the comment section)