Question

In how many ways can a string of length 5 be formed using the letters ABCDEFG without repetitions. It should begin with the letter F and end with the letter A. 

Answer 1

To solve this problem we should multiply the number of options for each letter of the string(from 1 to 5)

On the first place is certainly F and on the last is certainly A, so now the point is to find out in how many ways can a 3-letter string be formed using letters BCDEG without replacement

Let A be the number of ways, then

$A=5*4*3=60$ ways