statistic permutation and combonations

Question

Serial numbers for a product are to be made using 2 letters followed by 4 numbers. If the letters are to be taken from the first letters of the alphabet with no repeats and the numbers are taken from the digits 0 through 9 with no repeats, how many serial numbers can be generated?

Answer 1

The question is a bit ambiguous as what does it mean from 'the first letters of the alphabet'? I will assume this to mean the first half of the alphabet. This gives 13 letters. So there are 13 choices for the first letter and 12 choices for the second (we are not allowed to repeat the letter we chose for the first). This gives 13*12 choices for the first two letters. Now there are 10*9*8*7 choices for the numbers (10 choices, namely 0,1,2,3,4,5,6,8,9 for the first number, but only 9 for the second since we cannot repeat the previous number and so on). 

 

We need to choose two letters AND 4 numbers. So this gives (13*12)*(10*9*8*7)=786,240 total possible serial numbers.