Answer to Question #278363 in Discrete Mathematics for mickey

Question

Ask about the lenght of 5 formed using the lettre ABCDEFG without repetitions. How many string begins with the letter F and end with the letter A

Answer 1

It follows that that by Combinatorial Product Rule the number of strings of length 5 which consist of the letters A, B, C, D, E, F and G without repetition is equal to $7\cdot6\cdot 5\cdot4\cdot 3=2,520.$ The number of strings of length 5 without repetition which begins with the letter F and end with the letter A is equal to $5\cdot 4\cdot 3=60.$