posted by joey on .
a book club assigns to each member a membership number that consists of 2 letters followed by 4 numbers. how many different membership numbers are possible. tne membership numbers look like XXxxxx where X are letters and x are letters.
26 letters in the alphabet
10 numbers (0-9)
An easy way to think about it is like this:
If you have one number there are ten possible numbers (0-9). If you have two numbers you know that there are 10 possible numbers for each position (00-99), which is 10*10 .
Letters have 26 values (a-z) or 52 values (a-z and A-Z). Using what we learned from numbers, if we multiply the number of letters in the alphabet by the number of possible letters we will get the number of results (26*26).
26*26 + 10*10*10*10 = 10,676
This can also be written as:
26^2 + 10^4 = 10,676