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- Permutations and Combinations

Still Confused?

Try reviewing these fundamentals first.

Still Confused?

Try reviewing these fundamentals first.

Nope, I got it.

That's that last lesson.

Start now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started Now- Lesson: 17:16
- Lesson: 2a8:39
- Lesson: 2b4:37
- Lesson: 2c2:41
- Lesson: 2d1:02
- Lesson: 2e1:37
- Lesson: 2f3:39
- Lesson: 3a30:19
- Lesson: 3b13:29
- Lesson: 3c10:05
- Lesson: 4a9:35
- Lesson: 4b3:38
- Lesson: 4c6:20
- Lesson: 4d5:26
- Lesson: 5a3:20
- Lesson: 5b3:22
- Lesson: 5c9:59

How many choices do I have? This lesson can help you with answering this question! Combination is the process of selecting members from a set of items. Combination formula is your best friend in this lesson. Unlike permutations, order doesn't matter in combinations!

Basic concepts: Simplifying rational expressions and restrictions, Solving rational equations, Permutation vs. Combination,

? combination: nCr = number of selections of r items taken from a set of n distinct items (order does NOT matter!!)

= $\frac{{n!}}{{(n - r)!\;\;r!}}$

= $\frac{{n!}}{{(n - r)!\;\;r!}}$

- 1.Compare the difference between the following 2 scenarios:a)How many ways can a president, a vice president, and a treasurer be selected from a class of 20 students?b)How many different committees of 3 people can be selected from a class of 20 students?
- 2.A standard deck of 52 cards consists of:

• 4 suits: diamonds, hearts, spades, and clubs

• each suit has 13 cards

• red cards: diamonds and hearts

• black cards: spades and clubs

• face cards: Jacks, Queens, and Kings

How many different 5-card hands can be formed containing:a)any 5 cards (no restrictions)?b)all black cards?c)1 black card and 4 red cards?d)all face cards?e)3 Jacks and 2 Kings?f)3 Jacks? - 3.? problems with "at least", "at most"

From a standard deck of 52 cards, how many different 5-card hands can be formed containing:a)exactly 2 Diamonds?b)at least 2 Diamonds?c)at most 2 Diamonds? - 4.There are 20 members in a student council, 7 boys and 13 girls. How many ways can a committee of 5 people be selected if there must be:a)at least 3 boys?b)at most 1 girl?c)at least 1 girl?d)at least 2 boys and 2 girls?
- 5.Five points are marked on a circle. By connecting the points on the circle,a)How many triangles can be formed?b)How many line segments can be formedc)Form a pentagon inside the circle by connecting the 5 points. How many diagonals does the pentagon have?

We have over 1420 practice questions in College Algebra for you to master.

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