Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

CSE 103 > Lec 3: Basic Combinatorics > Flashcards

Lec 3: Basic Combinatorics Flashcards

1
Q

What are sets in these forms:

  1. Explicit
  2. Implicit
  3. Intersection
  4. Union
A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

What is the product of sets?

A

Taking all possible combinations

| color | = 2

| size | 5

size of produce set = 3 x 2 x 5

style | == size of set style = 3

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

What is raising a set to a power?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What is the factorial function?

A

The number of way to order n objects in n!

The number of possible ways to put n different objects into n different slots is

n * (n-1) * (n-2) * … * 2 * 1 = n!

  • so n factorial
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

When do we use permutations?

A

How many ways are there to pick k out of n elements when the order matters

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

What is the permutation function?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

When do we use combinations?

A

How many ways are there to pick k out of n elements when the order does not matter

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

How many ways are there to pick 3 out of 7 elements when order does not matter?

A

C (3, 7)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

What is the combinatorial function?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q
A

C(3,7) or C(4,7)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

How many different 3 digit numbers from the digits 1-9?

A

2 2 1

9 x 9 x 9 = 9^3

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

How many different 4 digit numbers from the digits 1-9 where all of the digits are different?

A

Permutation

  • P (9, 4) = 9!/ (9-4)!
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

How many different 4 digit numbers from the digits 1-9 where all of the digits are different and the digits are in increasing order?

A
  • when the order is fixed, order doesn’t matter
  • combinatorics
  • C(9,4) = 9!/(4!5!)
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

Suppose you choose 4 different digits from the set 1-9 and you place them in increasing order. What is the probability that the first digit is 3?

what is the size of the sample space?

What is the size of the event?

A
  • P(A) = |A|/|omega|
  • What is the size of the sample space?
  • |omega| = C(9,4) = 9!/(4! 5!)
  • What is the size of the event?
  • |A| = C(6,3)
  • Probability?
  • P(A) = [C(6,3)]/[C(9,4)]
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

How many different words can be created by rearranging (all) the letters in the word MISSISSIPPI?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

Suppose the letters of the word MISSISSIPPI are put in a random order. What is the probability that the result is again MISSISSIPPI?

What is the size of the sample space?

What is the size of the event?

A
  • What is the size of the sample space?
    • 11!
    • Why 11! instead of C(11 4,4,2,1)?
      • when we say we’re taking a random word ordering in the outcome space, the objects are all distinguishable
  • What is the size of the event?
    • 1!4!4!2! b/c 1 M, 4 I’s, 4 S’s, 2 P’s
  • Probability is
    • P(event) = | event | / | sample space |
    • P(A) = 4!4!2!)/11!
17
Q

A fair coin is flipped 11 times, what is the probability of 4 heads and 7 tails?

What is the size of the sample space?

What is the size of the event?

A

CSE 103 (10 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions