A company issues 7digit ID numbers to each of its employeesH

A company issues 7-digit ID numbers to each of its employees.How many ID numbers can be made if the following criteria must all be met:

The first two digits must be 21 or 31.

No number may be repeated.

The last number must be a 5 or a 6.

Solution

7 digit numbers can take the following 4 forms

21----5, 21----6

31----5, 31----6

each with a probability of 1*1*7*6*5*4*1 , so total ID numbers = 4*(1*1*7*6*5*4*1) = 4*42*20 = 3360