A standard deck of playing cards contains 13 spades. In how many distinct orders can these 13 spade cards alone be arranged in a row?

Introduction / Context:
This question is a simple test of your understanding of permutations of distinct objects. Each spade card in a deck is different from the others, so arranging them in a sequence is a straightforward example of counting permutations with no repetition.

Given Data / Assumptions:

• The deck has 13 different spade cards (for example, Ace of Spades, 2 of Spades, up to King of Spades).
• All 13 spade cards are distinct.
• We want to count the number of different orderings of these 13 cards in a row.

Concept / Approach:
When you arrange n distinct objects in a line and every arrangement is considered different, the number of possible arrangements is n factorial (n!). This arises because there are n choices for the first position, (n - 1) choices for the second, and so on, down to 1 choice for the last position. Multiplying these gives n!.

Step-by-Step Solution:
There are 13 distinct spade cards.The number of permutations of 13 distinct objects = 13! (13 factorial).13! means 13 * 12 * 11 * ... * 2 * 1.We do not need to compute the exact numerical value here because the expression 13! itself represents the correct count.

Verification / Alternative check:
If you wanted, you could compute the approximate size of 13! to get a sense of magnitude, but for exam purposes recognizing 13! as the permutation count is sufficient.No division by factorials is needed because there are no repeated cards.

Why Other Options Are Wrong:
13^2 (13 squared) counts something like choosing among 13 cards with replacement for only 2 positions, which is unrelated.13^13 represents a different model where each of 13 positions could take any of 13 cards with repetition allowed, which is not our situation.2! only counts the number of permutations of 2 items and is far too small.

Common Pitfalls:
Confusing exponent notation with factorial notation.Assuming some symmetry or repetition among cards that does not exist.Trying to divide by something because in many word problems letters repeat; here they do not.

Final Answer:
The number of distinct arrangements is 13!.