Exam 3

Question 1

How do you find the sum of the nth row?

Answer 1

2^n

Question 2

What is row 0 of pascals triangle

Answer 2

1

Question 3

what is row 1 of pascals triangle

Answer 3

1 1

Question 4

what is row 2 of pascals triangle

Answer 4

1 2 1

Question 5

what is row 3 of pascals triangle

Answer 5

1 3 3 1

Question 6

what is row 4 of pascals triangle

Answer 6

1 4 6 4 1

Question 7

what is row 5 of pascals triangle

Answer 7

1 5 10 10 5 1

Question 8

what is row 6 of pascals triangle

Answer 8

1 6 15 20 15 6 1

Question 9

what is row 7 of pascals triangle

Answer 9

1 7 21 35 35 21 7 1

Question 10

what is row 8 of pascals triangle

Answer 10

1 8 28 56 70 56 28 8 1

Question 11

How do you find the # of subsets that an asset with n elements has?

Answer 11

2^n

Question 12

What is a powerset

Answer 12

set of all subsets

Question 13

What does a ∩ b mean

Answer 13

Intersection. The intersection of two sets is a new set that contains all of the elements that are in both sets.

Question 14

what does a ∪ b mean

Answer 14

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 ”.

Question 15

What does B’ mean

Answer 15

everything that is not inside B

Question 16

How do you find the number of bit strings in length n?

Answer 16

2^n

Question 17

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)

Answer 17

ex: do 9 nCr 5 (length 9 with exactly 5 1s and 4 0s)

Question 18

What does 3! mean

Answer 18

321 (6 permutations)

Question 19

What is the formula for permutations

Answer 19

n! = n(n-1)(n-2_..(3)(2)(1)

Question 20

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)

Answer 20

1 (1,2) 2 3 4

4!2! = 48

Question 21

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)

Answer 21

You take the compliment (total - opposite)

5!-4!-2!

Question 22

What is the formula for the compliment

Answer 22

total - opposite

Question 23

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)

Answer 23

3!3!

5-3 = 2 + 1 (1 group of 3)) x (amount that needs to be together

Question 24

When calculating in a horse race with 9 horses, how many ways can the top 3 finish?

Answer 24

Use nPr so 9p3 = 504

of permutations of n things taken # at a time

Question 25

What if each 0 in a length 9 bit string must be immediately followed by a 1? (4 zeros)

Answer 25

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