Counting Principles Flashcards
It refers to the set of all outcomes in an experiment
Sample space
It states that if k outcomes are mutually exclusive and outcome 1 can occur in m1 ways, outcome 2 can occur in m2 ways and so on, then the total number of outcomes is
m1 + m2 + … + mk
Addition rule
A developer of a new subdivision offers prospective home buyers a choice of Tudor, rustic, colonial, and traditional exterior styling in ranch, two-story, and split-level floor plans. In how many different ways can a buyer order one of these homes?
Sam is going to assemble a computer by himself. He has the choice of ordering chips from two brands, a hard drive from four, memory from three, and an accessory bundle from five local stores. How many different, ways can Sam order the parts?
Five chips numbered 1 to 5 are in a container. You are asked to get 3 chips from the container, one at a time. In how many ways can this experiment be performed or how many possible outcomes are there if sampling is done without replacement? with replacement?
Consider the same problem as in above but this time, you are to get only one chip from the container. If the number on the chip is even, you have to roll a die. On the other hand, if the number on the chip is odd, you have to toss a coin. How many possible outcomes are there in this experiment?
- 2.
How many even four-digit numbers can be formed from the digits 0, 1, 2, 5, 6, and 9 if each digit can be used only once?
Three boys and three girls are to sit in 6 chairs arranged in a straight line. How many seating arrangements are possible if:
a. there are no constraints?
b. if the group of boys and the group of girls are each to sit together
c. if boys and girls are to alternate?
d. if only the boys must sit together
e. two girls quarrelling over one guy refuse to sit beside each other?
f. The 3 boys and 3 girls actually form 3 couples. How many seating arrangements are possible if couples should sit beside each other?
g. How many arrangements are possible if 3 people prefer to be seated together?
Given the numbers 0,1,2,3,4,5,6,7,8,9
a. How many 3 digit numbers can be formed without repetition?
b. How many are odd?
c. How many of these 3 digit numbers are even?
d. How many of these numbers are greater than 342?
e. How many of the numbers greater than 342 are even?
d. How many 3 digit numbers can be formed with repetition?
The probability of occurrence of both the events A and B is equal to the product of the probability of B occurring and the conditional probability that event A occurring given that event B occurs.
Multiplication Rule
Regular deck of cards
Total - 52 cards
Suits - 4 (Clubs, Diamonds, Hearts, Spades); Each suit has 13 cards
13 cards - Ace, 9 cards, Jack, Queen, King
An arrangement of all part of a set of distinct objects where order matters
Permutation
A president and a treasurer are to be chosen from a student club consisting of 50 people. How many different choices of officers are possible if
there are no restrictions;
a. A will serve only if he is president;
b. B and C will serve together or not at all:
c. D and E will not serve together?
In how many ways can you arrange the 5 letters A, B, C, D and E if you take:
a. 2 letters at a time?
b. 3 letters at a time?
3. 4 letters at a time?
4. all letters at the same time?
It refers to the subset of all objects where the order doesn’t matter
Combination
Consider 3 letters A, B and C. How many combinations of 2 letters are possible?
3
