Question

find the number of distinguishable permutations of the letters LUCKY.

Answer 1

how did you get that?

Answer 2

which of course does not mean the answer is emphatically 5 but means
\[5!=5\times 4\times 3\times2\]

Answer 3

5 choices for first letter
4 choices for second
3 choices for third
2 choices for 4th
1 choice for last
counting principle says number of way to do this together is the product of the number of ways to do each one