Download presentation

Presentation is loading. Please wait.

Published byRobyn Edgecomb Modified over 2 years ago

1
Combinations A combination is a grouping of things ORDER DOES NOT MATTER

2
How many arrangements of the letters a, b, c and d can we make using 3 letters at a time if order does not matter? We know there are 4! = 24 permutations. Listed out they are: abc acb bac bca cab cba = 1 combination abd adb bad bda dab dba = 1 combination acd adc cad cda dac dca = 1 combination bcd bdc cbd cdb dbc dcb = 1 combination = 4 combinations, total

3
Each of the above combinations had 3 letters, so there were 3! ways to change the order around (3! permutations). If order doesnt matter we will divide by that number. Each of the above combinations had 3 letters, so there were 3! ways to change the order around (3! permutations). If order doesnt matter we will divide by that number. The number of ways of choosing r objects from a set of n without regard to order is: This is commonly read as n choose r

4
Two examples to show the difference between permutations and combinations: How many seating arrangements of 6 students can be made from a class of 30? (order matters – a permutation) How many seating arrangements of 6 students can be made from a class of 30? (order matters – a permutation)

5
How many ways are there of choosing 6 students for a class project in a class of 30? (order does not matter – just that 6 students are picked – a combination)

6
How many different 6 number lottery tickets can be issued? A purchaser picks 6 numbers from 00 – 99 and it does not matter which order they are in. How many different 6 number lottery tickets can be issued? A purchaser picks 6 numbers from 00 – 99 and it does not matter which order they are in.

7
100 numbers to pick from Want the 6 that are correct Picking 6 correct lottery numbers...

8
How many different 5-card poker hands are there?

9
52 cards to pick from Want 5 cards total Different 5-card poker hands...

10

11
How many different 5-card hands can there be if all cards must be clubs (a flush in clubs)?

12
13 clubs to pick from Want 5 cards total A flush in clubs...

13
How many different 5-card hands can there be if all cards must be the same suit (a flush in any suit)?

14
A flush in ANY suit... 4 cases that are the same - the 4 cases are from the 4 suits: hearts, spades, clubs or diamonds. Same as the previous example

15
How many different 5-card hands can there be that contain exactly 3 Aces?

16
# ways to get 3 Aces * # ways to get other 2 cards 5 cards with exactly 3 aces...

17
How many different 5-card hands can there be that contain at least 3 Aces?

18
# ways to get 3 Aces (from previous example) + # ways to get 4 Aces 5 cards with at least 3 aces... = = 4560 ways

19
How many different 5-card hands can there be that contain exactly 2 Hearts?

20
# ways to get 2 Hearts * # ways to get other 3 cards 5 cards with exactly 2 hearts...

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google