Download presentation

Presentation is loading. Please wait.

1
**Combinations Examples**

Example 1: From a group of 10 books, how many different pairs can you choose to take on your next trip?

2
**Combinations Examples**

Example 1: From a group of 10 books, how many different pairs can you choose to take on your next trip? C(10, 2) = (10•9)/2 = 45

3
**Combinations Examples**

Example 2: From a group of 10 books, how many different groups of 3 can you choose to take on your next trip?

4
**Combinations Examples**

Example 2: From a group of 10 books, how many different groups of 3 can you choose to take on your next trip? C(10, 3) = (10•9•8)/(3!) = 120

5
**Combinations Examples**

Example 3: From a group of 10 books, how many different groups of 4 can you choose to take on your next trip?

6
**Combinations Examples**

Example 3: From a group of 10 books, how many different groups of 4 can you choose to take on your next trip? C(10, 4) = (10•9•8•7)/(4!) = 210

7
**Combinations Examples**

Example 4: From a group of 10 books, how many different groups of 6 can you choose to take on your next trip?

8
**Combinations Examples**

Example 4: From a group of 10 books, how many different groups of 6 can you choose to take on your next trip? C(10, 6) = (10!)/(4!6!) = 210 (Notice that C(10, 6) = C(10, 4). Why?)

9
**Combinations Examples**

Example 5: You’ve chosen to buy a large sundae with vanilla ice cream. You can choose 1, 2, or 3 toppings from a total of 7 available toppings. In how many different ways can you top your sundae?

10
**Combinations Examples**

Example 5: You’ve chosen to buy a large sundae with vanilla ice cream. You can choose 1, 2, or 3 toppings from a total of 7 available toppings. In how many different ways can you top your sundae? 1 Topping: C(7, 1) = 7 2 Toppings: C(7, 2) = 21 3 Toppings: C(7, 3) = 35 Total Possibilities: = 63

11
**Combinations Examples**

Example 6: A standard deck of cards contains 52 cards to include the numbers 2-10, a Jack, Queen, King, and Ace in each of four suits: Hearts and Diamonds are red, Spades and Clubs are black. In how many ways can you get 4 of a kind?

12
**Combinations Examples**

Example 6: A standard deck of cards contains 52 cards to include the numbers 2-10, a Jack, Queen, King, and Ace in each of four suits: Hearts and Diamonds are red, Spades and Clubs are black. In how many ways can you get 4 of a kind? There are 13 possibilities for face value: The numbers 2-10, a face card, or the Aces. The 5th card could be any of the remaining 48 cards in the deck. 13(48) = 624

13
**Combinations Examples**

Example 7: A standard deck of cards contains 52 cards to include the numbers 2-10, a Jack, Queen, King, and Ace in each of four suits: Hearts and Diamonds are red, Spades and Clubs are black. In how many ways can you get 3 of a kind?

14
**Combinations Examples**

Example 7: A standard deck of cards contains 52 cards to include the numbers 2-10, a Jack, Queen, King, and Ace in each of four suits: Hearts and Diamonds are red, Spades and Clubs are black. In how many ways can you get 3 of a kind? There are 13 possible face values, as in the previous example. However, we have more than 1 way to combine each value. For example, there are C(4, 3), or 4 ways to have 3 Aces. Continued… ↘

15
**Combinations Examples**

Example 7: A standard deck of cards contains 52 cards to include the numbers 2-10, a Jack, Queen, King, and Ace in each of four suits: Hearts and Diamonds are red, Spades and Clubs are black. In how many ways can you get 3 of a kind? Say we have 3 Kings. Neither the 4th nor the 5th card can be a King, because that would give us 4 of a kind. Also, the 4th and 5th cards cannot have the same face value, which would result in a full house. There are C(12, 2) = 66 possible pairings of face values, and each card can be any suit. This gives us 4(13)(66)(42) = 54,912 possibilities.

16
**Combinations Examples**

Example 8: A flush consists of 5 cards of the same suit. How many flushes are possible in a deck of cards?

17
**Combinations Examples**

Example 8: A flush consists of 5 cards of the same suit. How many flushes are possible in a deck of cards? There are 4 suits. Within each suit, there are C(13, 5) = 1287 combinations of 5 cards. However, we should exclude the 10 possible straight/royal flushes in each suit. Thus there are 4(1277) = 5108 possible flushes.

18
**Combinations Examples**

Example 9: A straight flush consists of 5 cards in order and of the same suit, such as J-Q of Diamonds. How many straight flushes are possible in a deck of cards?

19
**Combinations Examples**

Example 9: A straight flush consists of 5 cards in order and of the same suit, such as J-Q of Diamonds. How many straight flushes are possible in a deck of cards? If we arrange the cards from lowest value to highest, then we have 9 starting points: A-9 (A through 9-10-J-Q-K, excluding 10-J-Q-K-A because that is a royal flush). Because we have 4 suits, there are a total of 9(4) = 36 possible straight flushes.

20
**Combinations Examples**

Example 10: A straight consists of 5 cards in order, such as J-Q. How many straights are possible in a deck of cards?

21
**Combinations Examples**

Example 10: A straight consists of 5 cards in order, such as J-Q. How many straights are possible in a deck of cards? We can arrange the cards again from lowest to highest, starting with A-10, which gives us 10 possible sets of face values. We can have any combination of suits, as long as we don’t have 5 of the same suit—which would be a straight flush. (Continued on next slide)

22
**Combinations Examples**

Example 10: A straight consists of 5 cards in order, such as J-Q. How many straights are possible in a deck of cards? Consider the straight , for example. There are 4 possibilities for the 6, because it can be any suit. Likewise there are 4 possibilities each for the 7, 8, 9, and 10. We don’t want all cards to be the same suit, though, so subtract the 4 possibilities of that (4 hearts, or 4 diamonds, etc.). (Continued on next slide)

23
**Combinations Examples**

Example 10: A straight consists of 5 cards in order, such as J-Q. How many straights are possible in a deck of cards? So we have 10 possible groupings of face values, and 45 – 4 = 1020 possible combinations of cards within each of those face value groupings. This gives us a total of 10(1020) = 10,200 straights, not including straight flushes or royal flushes.

Similar presentations

OK

Counting Techniques 1. Sequential Counting Principle Section 10.1 2.

Counting Techniques 1. Sequential Counting Principle Section 10.1 2.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Well made play ppt on website Ppt on viruses and bacteria pictures Ppt on statistics for class 11 maths Ppt on sf6 gas circuit breaker Ppt on power system Ppt on credit policy pdf Ppt on polynomials in maths what does the range Ppt on indian national political parties Ppt on rural livelihood in india Ppt on mother's day of class 11