Problem Solving

A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4
and 5, which can be repeated. If the product of the digits in the area code must be even, how many different
codes can be created?

26

venmic wrote:A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4
and 5, which can be repeated. If the product of the digits in the area code must be even, how many different
codes can be created?

26

_,_,_; now since each of the 3 blank spaces is to be filled either with 2,4,5 therefore there are total 3 ways for filling the each blank space, when no restriction is placed, then total no. of codes that can be generated will be 3*3*3=27;
out of these 27 numbers, we have counted 1 odd number which will occur when all the digits will be odd, i.e.(555), so total no. of codes whose product is even= 27-1=26..!!!