Prems and Coms PA HW

Question 1

The easy way means is comprised of 6 bases, 18 flavours and 9 toppings. To order, let us assume that a person must choose 1 base, 1 flavour and 1 Topping. A person can also choose whether to order a regular or large drink. Additionally, a person may choose to ice or not.
How many different drinks can Easy Way Edward order?

Answer 1

3888

Question 2

Isuru then decides to ask Edward to buy him a drink from EasyWay. He tells Edward to buy him any drink that contains lychee or passionfruit as a flavor. Edward instead ordered a completely random combination for isuru.
How many possible drinks satisfy Isuru’s conditions?

Answer 2

432

Question 3

What is the probability that Edward’s random drink satisfies Isuru’s conditions

Answer 3

1/9

Question 4

Edward buys a lychee, a taro, a honey and a strawberry flavoured drink, Edward now takes one drink for himself at random, and gives the remaining three drinks to three friends.
What is the probability that his friends with receive their respective flavours, given it is distributed randomly?

Answer 4

1/24

Question 5

A fair dice is rolled fours times. The numbers shown are then multiplied. How many different odd numbers can be produced?

Answer 5

15

Question 6

A prize would be won if anyone throw at least one double six simultaneously in 25 throws. If 100 people compete how many are expected to win the prize?

Answer 6

51

Question 7

A hand of 5 cards is dealt from a fair pack of 52 cards. What is the probability of being dealth a flush? (five cards from the same suit)

Answer 7

33/16660

Question 8

The numbers 1,2,…..,15 are arranged randomly in a line. What is the probability that the number 3 is left of the number 13?

Answer 8

1/2

Question 9

If n fair dice are rolled together, what is the probability that the product of the n scores is an even number?

Answer 9

(2^n -1)/2^n

Question 10

How many ways can 5 letters be chosen form the letters of the word ARRANGE?

Answer 10

12

Question 11

In how many ways can the letters of WOOLLOOMOOLOO be arranged if there is to be no repetition?

Answer 11

25740

Question 12

Number plates now have two letters, followed by two numbers, followed by another two letters (e.g BE-19-0N) How many possible number plates are there in this format?

Answer 12

45697600

Question 13

A parent-teacher night interview consists of two teachers, three parents and five children sitting around a circular table.
How many possible arrangements are three if:
a) there is no restictions
b)the teachers must sit together
c) The children care not to sit together

Answer 13

362880
80640
2880

Question 14

A bag consist of 10 red marbles, 4 white marbles, and 6 black marbles. Three marbles ar selected at random without replacement. What is the probability that

a) all marbles are red
b) no marbles are red
c) all marbles are of different colours

Answer 14

2/9
2/19
4/19

Question 15

Twenty people are split into four groups of five people for a tournament.

a) in how many ways can the groups be formed?
b) IF the groups have been formed, in how many ways can the twenty people be arranged in a straight line such that the four groups stay together?

Answer 15

488864376

4976640000

Question 16

The letters of the word BETWEEN are arranged in a line. How many ways can they be arranged if:

a) all the E’s are together?
b) all the E’s are separated?
c) the consonants are in alphabetical order from left to right, but not necessarily together?

Answer 16

120
240
35

Question 17

The entrance to a bank vault consists of 12 switches, each of h can be set to one of three positions.

a) how many total ways can these switches be arranged?
b) what is the probability that if all the switches are set randomly, there will be an equal number in each position?

Answer 17

531441

3850/59049

Question 18

A box of contains chocolates, two of which are identical. From this box, three chocolates are drawn without replacement.

a) How many different selections could be made?
b) What is the probability that a selection will include the two identical chocolates

Answer 18

14

2/7

Question 19

A binary string is a sequence of 1s and 0s
In a binary string a length 50, how many ways are there to have a string with exactly nine 1’s such that no two 1’s are adjacent?

Answer 19

445891810

Question 20

30 identical gold coins are randomly placed into 10 identical wooden boxes. A box contains anywhere from 0 to 30 coins.

a) how many total possible ways can the 30 coins be placed into the boxes?
b) How many possible arrangments are there if each bob must have at least one coin?

Answer 20

a) 2119125132

b) 10015005

Question 21

Aidan drives exactly 10 blocks ( only right and down) from A to B. (corner to corner on 4x6 grid)

a) how many different routes aidan can drive home?
b) How many different routes if he wishes to stop by KFC (2d,2r)
c) If Aidan takes random route home, is he more likely to drive past KFC or Maccas?

Answer 21

210

Question 22

A council has 14 people, 6 labor, 5 liberal, 3 independents. Five are chosen at random to form a committee.

a) how many different groups can be formed
b) Probability it will have majority labor
c) How many if at least one councilor from each of the three parties is 1365.
d) Given that the committee contains at least one councilor from each party, find the probability that it will be majority labor.

Answer 22

2002
49/143
1365
20/91

Question 23

A box contains n jellybeans, some white and some black. Saf and Isuru take turns picking a jellybean from the box, without looking, until the box is empty. Isuru picks first.
a) IF there are 1 black and n-1 white white jellybeans and n is odd, show that the probability that isuru picks the black jellybean is given by n+1/2n

b) If there are 2 black and n-2 white jelly beans and n is even, show that the probability that isuru is the first to pick a black jellybean is given by n/2(n-1)
c) If there are 2 black and n-2 white jelly beans and n is odd, show that the probability that isuru is the first to pick a black jellybean is given by n+1/2n

Answer 23

Proof