SOLUTION: How many different 7-place license plates are possible if the first 4 places are for the letters (A, B, C, D, E, F) and the other 3 for numbers if the repetitions are not available

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Question 1205978: How many different 7-place license plates are possible if the first 4 places are for the letters (A, B, C, D, E, F) and the other 3 for numbers if the repetitions are not available?
Answer by Edwin McCravy(20063) About Me  (Show Source):
You can put this solution on YOUR website!
Look at an example, say this one:

DFAC470

Choose a letter to go where the D is in any of 6 ways. 
Choose a letter to go where the F is in any of 5 ways. 
Choose a letter to go where the A is in any of 4 ways. 
Choose a letter to go where the C is in any of 3 ways. 
Choose a digit to go where the 4 is in any of 10 ways. 
Choose a digit to go where the 7 is in any of 9 ways. 
Choose a digit to go where the 0 is in any of 8 ways. 

Multiply all those numbers of ways together:
You'll get a 6-digit number.

Edwin