Permutation and Factorial Notation

[ksmytaniuk]

First, I'd like to apologize if my post is in the wrong section of this forum. I'm still getting used to all the subforums here.

Anyways, I'm a student that's been out of school for 6 years but am now taking a math upgrade class to apply for a post-secondary course. I live in Saskatchewan, Canada and our curriculum has been modified so there is only 1 math level required for post-secondary application. What I'm taking is called Foundations of Mathematics 30 Level. It includes pre-calculus.

The unit I'm working on right now deals with Permutations and Factorial Notation. I'm struggling with the concept of simplifying notations within algebraic equations. Below I've posted the current assignment I'm working on. Any help or insight will be greatly appreciated!

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. . . . .Section 4.2 and 4.3 Handin Assignment

1. Solve \(\displaystyle \, \dfrac{(n\, +\, 3)\, (n\, +\, 2)!}{(n\, +\, 1)!}\, =\, 30\)

My work:

. . . . .\(\displaystyle \color{blue}{\dfrac{(n\, +\, 3)\, \bigg[(n\, +\, 2)\, (n\, +\, 1)\bigg]}{(n\, +\, 1)}\, =\, 30} \)

. . . . .\(\displaystyle \color{blue}{(n\, +\, 3)\, (n\, +\, 2)\, =\, 30}\)

. . . . .\(\displaystyle \color{blue}{n^2\, +\, 5\, =\, 30}\)

2. How many different permutations are there of 5 objects from a set of 7 different objects, if repetition is not allowed?

3. Marta is writing a science-fiction story in which the serial number of a starship can have one, two, or three different letters, followed always by four different numerals. How many different starship serial numbers are possible?

 

[Mrspi]

First, I'd like to apologize if my post is in the wrong section of this forum. I'm still getting used to all the subforums here.

Anyways, I'm a student that's been out of school for 6 years but am now taking a math upgrade class to apply for a post-secondary course. I live in Saskatchewan, Canada and our curriculum has been modified so there is only 1 math level required for post-secondary application. What I'm taking is called Foundations of Mathematics 30 Level. It includes pre-calculus.

The unit I'm working on right now deals with Permutations and Factorial Notation. I'm struggling with the concept of simplifying notations within algebraic equations. Below I've posted the current assignment I'm working on. Any help or insight will be greatly appreciated!

I'll deal with the first problem, since that is the only one you have showed any work for......

[(n + 3)(n + 2)!] / (n + 1)! = 30

You can't just "forget" the exclamation points, which are the notation used to indicate factorials! So, I'll keep putting them in as long as they apply.

(n + 2)! means (n + 2)(n + 1)!, so we can rewrite the numerator:

[(n + 3)(n + 2)(n + 1)!] / (n + 1)! = 30

And we can divide out the common factor of (n + 1)! which appears in the numerator AND the denominator of the fraction, leaving

(n + 3)(n + 2) = 30

And you got there.....but after that, I see trouble.

Have you learned how to multiply binomials?
(a + b)(c + d) = (a + b)*c + (a + b)*d, or
= ac + bc + ad + bd

You might want to review some websites with lessons on multiplying binomials.....

Apply that pattern to (n + 3)*(n + 2).....you will NOT get n² + 5 = 30.

When you get the correct result for the multiplication, you'll be left with a quadratic equation to solve....and you will probably want to review methods for solving quadratic equations (there are lots of websites which cover that process, too).

After you've done some review and made some corrections, you can come back and show us what you've got.