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- Math 30-2 (Alberta)
- Permutations and Combinations

Still Confused?

Try reviewing these fundamentals first

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Try reviewing these fundamentals first

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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 plenty of practice questions in Math 30-2 (Alberta) for you to master.

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