Will must choose a 3-character computer password, consisting of 1 letter from the alphabet and 2 distinct digits, in any order.From how many different passwords can Will choose? Choose the correct answer:	A) 390	B) 2,340	C) 4,680	D) 7,020	E) 14,040
Take the task of creating a password and break it into stages.   Stage 1: Select the one letter to be used in the code   There are 26 letters from which to choose, so we can complete this stage in 26 ways.   Stage 2: Select the two digits to be used in the code   Since the order in which we select the two digits does not matter, we can use combinations.   We can select 2 digits from 10 women in 10C2 ways (45 ways)   So, we can complete stage 2 in 45 ways   NOTE: We now have the 3 characters to be used in the code. At this point, we need to arrange those 3 characters.   Stage 3: Arrange the 3 selected characters.   RULE: We can arrange n unique objects in n! ways.   So, we can arrange the 3 characters in 3! ways (6 ways)   So we can complete stage 3 in 6 ways.   By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create a password ) in (26)(45)(6) ways   (26)(45)(6) = 7020 ANS:7,020
<result>D</result>
Will must choose a 3-character computer password, consisting of 1 letter from the alphabet and 2 distinct digits, in any order.From how many different passwords can Will choose?