# There are 12 face cards in a standard deck of 52 cards. How many ways can you arrange a standard deck of 52 cards such that the first card is a face card?

There are a few ways to approach this - I'm going to use the one that makes sense to me (and hopefully to you!)

We start with knowing there are 52 cards in a deck of cards. We are asked for the number of ways we can arrange the cards such that a face card is the first. (Face cards are the King, Queen, and Jack of each of the four suits: Spades, Hearts, Clubs, Diamonds).

Let's start with the King of Spades as the first card. We can now arrange the remaining 51 cards any way we want. When we arrange cards any way we want, we use the Factorial calculation. So that's 1 card arranged any way we want multiplied by 51 cards arranged any way we want:

We can do this calculation 12 times - once for each of the 12 Face Cards in the front of the deck, so that puts us at:

Which is an amazingly huge number. As an exercise as to just how big this number is, read the link below:

By signing up, you agree to our Terms of Service and Privacy Policy

There are 3,744 ways to arrange a standard deck of 52 cards such that the first card is a face card.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How many distinguishable ways can the letter of the word SASSAFRAS be arranged using all the letters?
- If you draw one card from a deck of cards, what is the probability that it is a heart or a diamond?
- In a statistics class there are 11 juniors and 6 seniors; 4 of the seniors are females, 6 of the juniors are males. If a student is selected at random, what is the probability that the student is either a senior or a male?
- How do you find the number of distinguishable permutations of the letters HONEST?
- The probability that a new spark plug is defective is 0.06. You need two new spark plugs. What is the probability that both spark plugs are defective?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7