# Permutations - Ordered pairs. Can you explain an answer?

• Dec 15th 2009, 11:20 AM
Kakariki
Permutations - Ordered pairs. Can you explain an answer?
I am doing homework, and I do not understand an answer the text is giving me. I know the answer is correct, but I do not understand how they get it using permutations.

Question: How many ordered pairs can be formed from set A without allowing the first number to be the same as the second number? (set A is: {2,3,4,5,7})

Since there are 25 ordered pairs that can be formed from this set n(A x A) = 25. I just subtract 5 from that because there are 5 ordered pairs that use the same number. So 20.

P (5,2) = 20
I do not understand how they get this answer. Can someone explain it for me? I have been racking my brains for a while now and do not understand how to get it.

The next question in the text is very similar, so it would be great if I understood how to do it, as seeing things alot usually means it will be on the exam!
• Dec 15th 2009, 12:07 PM
Plato
Quote:

Originally Posted by Kakariki
Question: How many ordered pairs can be formed from set A without allowing the first number to be the same as the second number? (set A is: {2,3,4,5,7}) Texts answer:
P (5,2) = 20
I do not understand how they get this answer.

By definition $\displaystyle ^NP_k=\frac{N!}{(N-k)!}$

So $\displaystyle ^5P_2=\frac{5!}{3!}=5\cdot 4 =20$
• Dec 15th 2009, 02:40 PM
Kakariki
Quote:

Originally Posted by Plato
By definition $\displaystyle ^NP_k=\frac{N!}{(N-k)!}$

So $\displaystyle ^5P_2=\frac{5!}{3!}=5\cdot 4 =20$

Thank you for the reply! However, I must not have been very clear in my original post. I was meaning, given the question, how do you get the answer of P (5,2). I understand how permutations work, I just do not understand how to answer this specific question.

Like, they have ordered pairs, I am looking for an explanation of why they used permutations and HOW.
• Dec 15th 2009, 03:25 PM
Plato
Quote:

Originally Posted by Kakariki
Thank you for the reply! However, I must not have been very clear in my original post. I was meaning, given the question, how do you get the answer of P (5,2). I understand how permutations work, I just do not understand how to answer this specific question.

Like, they have ordered pairs, I am looking for an explanation of why they used permutations and HOW.

Well I am equally puzzled by you confusion!
There are five ways to choose the first term of the ordered pair and four ways to choose the second term.
Now by anyone’s understanding that is a permutation of five taken two at a time.

What about that do you not understand?
• Dec 15th 2009, 05:32 PM
Kakariki
Quote:

Originally Posted by Plato
Well I am equally puzzled by you confusion!
There are five ways to choose the first term of the ordered pair and four ways to choose the second term.
Now by anyone’s understanding that is a permutation of five taken two at a time.

What about that do you not understand?

Oh!!! That clears it up. I was not thinking in terms of the number of ways to choose the first and second term. Thank you! It makes sense now. :)