Abelardo wants to create several different 7-character screen names. He wants to use arrangements of the first 3 letters of his first name(abe, followed by arrangements of 4 digits in 1984, the year of his birth. How many different screen names can he create in this way?
A.72
B.144
C.288
D.576
It's 144
The 'abe' can be arranged in 3! or 6 ways
the '1984' can be arranged in 4! or 24 ways
number of arrangements = ????
what do you think?
To find the number of different screen names Abelardo can create, we need to determine the number of arrangements for the different components of the screen name.
First, we need to consider the arrangements of the first 3 letters of his first name, "abe." Since all the letters are different, the number of arrangements is given by the formula for permutations of n objects, which is n!. In this case, n = 3, so the number of arrangements is 3! = 3 x 2 x 1 = 6.
Next, we need to consider the arrangements of the 4 digits in 1984. Similarly, since all the digits are different, the number of arrangements is 4!.
To calculate 4!, we multiply 4 x 3 x 2 x 1 = 24.
Now, to find the total number of screen names, we multiply the number of arrangements of the first name component (6) with the number of arrangements of the birth year component (24):
Total number of screen names = 6 x 24 = 144.
Therefore, Abelardo can create 144 different screen names in this way.
The correct answer is B. 144.