Question

The Greek alphabet contains 24 letters. How many fraternity names with Greek letters can be formed if each fraternity name contains 3 letters and repetition of letters is not permitted?
a)69
B)12144
c)13824

Answer 1

Slot method

1st slot=24 options
2nd slot=23 options (1 went to 1st slot)
3rd slot=22 options (another to previous slot)

multiply them
24*23*22=12144 ways

B

Answer 2

For the first letter we have 24 choices. Since letters can't repeat the second letter has 23 choices (24 minus 1 that was used for the first slot) and the third has 22 (24 minus one for the first slot and one for the second slot).

The total number of combinations is thus: 24 x 23 x 22= 12,144