Exam 3 Flashcards
How do you find the sum of the nth row?
2^n
What is row 0 of pascals triangle
1
what is row 1 of pascals triangle
1 1
what is row 2 of pascals triangle
1 2 1
what is row 3 of pascals triangle
1 3 3 1
what is row 4 of pascals triangle
1 4 6 4 1
what is row 5 of pascals triangle
1 5 10 10 5 1
what is row 6 of pascals triangle
1 6 15 20 15 6 1
what is row 7 of pascals triangle
1 7 21 35 35 21 7 1
what is row 8 of pascals triangle
1 8 28 56 70 56 28 8 1
How do you find the # of subsets that an asset with n elements has?
2^n
What is a powerset
set of all subsets
What does a ∩ b mean
Intersection. The intersection of two sets is a new set that contains all of the elements that are in both sets.
what does a ∪ b mean
The union of two sets is a new set that contains all of the elements that are in at least one of the two sets. The union is written as A ∪ B or “ A or B ”.
What does B’ mean
everything that is not inside B
How do you find the number of bit strings in length n?
2^n
How do you find the number of bit strings of length n that contain an exact amount of #? (length 9 with exactly 5 1s and 4 0s)
ex: do 9 nCr 5 (length 9 with exactly 5 1s and 4 0s)
What does 3! mean
321 (6 permutations)
What is the formula for permutations
n! = n(n-1)(n-2_..(3)(2)(1)
How do you calculate the number of permutations assuming 2 people must be adjacent (a group of 5 people but A and B need to be adjacent)
1 (1,2) 2 3 4
4!2! = 48
How do you calculate the number of permutations assuming 2 people cannot be adjacent (a group of 5 people but A and B cannot be adjacent)
You take the compliment (total - opposite)
5!-4!-2!
What is the formula for the compliment
total - opposite
How do you calculate the number of permutations assuming 3 people must be adjacent (a group of 5 people but A and B and C need to be adjacent)
3!3!
5-3 = 2 + 1 (1 group of 3)) x (amount that needs to be together
When calculating in a horse race with 9 horses, how many ways can the top 3 finish?
Use nPr so 9p3 = 504
of permutations of n things taken # at a time
What if each 0 in a length 9 bit string must be immediately followed by a 1? (4 zeros)
a (01) b (01) c (01) d (01) e
(9-4*1(4 groups of 01)) is c (5,1)
5 letters (a,b,c,d,e) with 1 combination of 01 because it can only ever be 1 combo regardless of position