Five character security codes for a store,are created by using a letter followed by 4 non-repeating numerical digits or using a digit followed by 4 non-repeating letters. The total number of security codes possible is?
My work:
Hqrscter security codes-a,b,c,d= 4 non repeating letters And 1,2,3,4= 4 non repeating digits There are 33463 number of security codes possible Is this the correct answer ? If not how do I solve this question,please help
For the first one which begins with a letter something I learned which is helpful but not always applicable is to draw boxes or lines to fill in representing how many choices you have at each stage : _ _ _ _ _ so if we want to fill in the first box we decide how many choices we have. If using English alphabet we would have 26 letter choices so we'd start with $\underline{26} $ _ _ _ _ then figure out our next decision which is a number so we would have 10 choices in base 10 so now we have made it to $ \underline{26} \ \underline{10}$ _ _ _ . Since we cannot repeat we would have 9 digits to choose from next $ \underline{26} \ \underline{10} \ \underline{9}$ _ _ again our next decision we cannot repeat so only 8 choices again similarly for the last step we only have 7 choices so the final answer in this examples would be $$26 \cdot 10 \cdot 9 \cdot 8 \cdot 7 $$ A similar approach would work for the second option you have to solve for.