Question

The access code for a? car's security system consists of five digits. The first digit cannot be 1 and the last digit must be even. How many different codes are? available? The number of different codes available is .

Answer 1

Total number of digits = 5

There are total 10 numbers in which there are 5 even numbers(i.e. 0, 2,4,6,8) & 5 odd numbers(i.e. 1,3,5,7,9)

Since, the first digit cannot be 1, there are nine possible numbers which correspond to the first digit.

The fourth, third and second digits have 0,1,2,3,4,5,6,7,8,9 as probable digits, meaning there are 10 possibilities for each.

Finally the last, 5th digit must be even. Therefore there are 5 possibilities.

By using the multiplication rule,the total number of possible combinations is :

(9)*(10)*(10)*(10)*(5)= 45000.

The number of different codes available is= 45000

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