Question

You are in charge of numbering the homes in a new subdivision, If we were to use 0 through 9 as our numbers to use and we want to have 3 digit house numbers, how many unique homes numbers would we potentially be able to provide?

1)What kind of a problem? permutation or combination

2)solve this problem

Answer 1

1. it is a problem of permutation. because here the order of the digits are also taken into account, as house with number 203 is different from that of number 230.

but in case of combination (2,3,0) and (2,0,3) would have been the same entity.

2. there are 10 digits: 0,1,2,3,4,5,6,7,8,9.

to form 3 digit numbers the first digit can be anything from 1 to 9. so total 9 cases.

for each such case, the second digit can be any one from 0 to 9. so 10 cases.

hence total 9*10=90 cases.

now for each such case the third digit can be any one from 0 to 9. so 10 cases.

hence total 90*10=900 cases.

So 900 unique homes numbers would we potentially be able to provide.