Basic Counting
What principle states that if you can do one task in m ways and another task in n ways, you can do both tasks in m × n ways?
What is the Multiplication Principle (or Fundamental Counting Principle)?
What does the notation ₍ⁿᵣ₎ or C(n,r) represent in counting problems?
What is the number of ways to choose r objects from n distinct objects regardless of order?
What is the notation P(n,r) or ₙPᵣ used to calculate?
What is the number of ordered arrangements of r objects selected from n distinct objects?
If the probability of an event occurring is 0.7, what is the probability of the event not occurring?
What is 0.3? (1 - 0.7 = 0.3)
The formula P(A|B) = P(A ∩ B)/P(B) is used to calculate what?
What is conditional probability? (The probability of event A occurring given that event B has occurred)
If you have 4 shirts, 3 pairs of pants, and 2 pairs of shoes, how many different outfits can you create?
What is 24 outfits? (4 × 3 × 2 = 24)
How many different committees of 3 students can be formed from a group of 10 students?
What is 120? (C(10,3) = 10!/(3!(10-3)!) = 120)
How many ways can 5 runners finish in 1st, 2nd, and 3rd place?
What is 60? (P(5,3) = 5!/(5-3)! = 60)
When rolling a fair six-sided die, what is the probability of rolling an even number?
What is 1/2 or 0.5? (3/6 = 1/2)
If two events A and B are independent, what is true about P(A|B)?
What is P(A|B) = P(A)? (For independent events, the conditional probability equals the probability of the event)
How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 if repetition is not allowed?
What is 60? (5 × 4 × 3 = 60)
A pizza shop offers 12 toppings. How many different 4-topping pizzas can be created?
What is 495? (C(12,4) = 12!/(4!(12-4)!) = 495)
How many different 4-letter code words can be formed using the letters of the word "ALGEBRA" without repeating any letter?
What is 840? (P(7,4) = 7!/(7-4)! = 840)
When drawing one card from a standard 52-card deck, what is the probability of drawing a face card (Jack, Queen, or King)?
What is 12/52 or 3/13? (12 face cards in a 52-card deck)
A bag contains 5 red marbles and 3 blue marbles. Two marbles are drawn without replacement. If the first marble drawn is red, what is the probability the second marble is also red?
What is 4/7? (After drawing a red marble, 4 red and 3 blue remain)
How many ways can 5 students be arranged in a line if 2 specific students must stand next to each other?
What is 48? (The 2 specific students count as 1 unit with 2! arrangements, so 4! × 2! = 48)
In how many ways can a 5-card hand be dealt from a standard 52-card deck?
What is 2,598,960? (C(52,5) = 52!/(5!(52-5)!) = 2,598,960)
In how many different ways can 8 people be seated around a circular table where seating arrangements that can be rotated are considered the same?
What is 5,040? ((8-1)! = 7! = 5,040)
What is the probability of being dealt a flush (5 cards of the same suit) in a 5-card poker hand?
What is approximately 0.00198 or about 1/508? (C(13,5)×4/C(52,5))
In a group of 25 students, 15 take math, 12 take physics, and 8 take both. If a student is selected at random and is known to take math, what is the probability they also take physics?
What is 8/15? (P(Physics|Math) = P(Math ∩ Physics)/P(Math) = 8/15)
How many different 7-character license plates can be made if the first 3 positions must be letters (A-Z) and the last 4 positions must be digits (0-9)?
What is 17,576,000? (26³ × 10⁴ = 17,576,000)
The formula ₍ⁿᵣ₎ = ₍ⁿₙ₋ᵣ₎ demonstrates what property of combinations?
What is the symmetry property? (Choosing r objects from n is the same as choosing n-r objects from n)
How many ways can the letters of the word "MISSISSIPPI" be arranged?
What is 34,650? (11!/(4!×4!×2!) = 34,650) - accounting for repeated letters
Two fair dice are rolled. What is the probability of rolling a sum of 7 or 11?
What is 8/36 or 2/9? ((6 ways to get 7 + 2 ways to get 11)/36 total outcomes)
Two events A and B have P(A) = 0.6, P(B) = 0.5, and P(A ∩ B) = 0.2. What is the probability of A given B?
What is 0.4? (P(A|B) = P(A ∩ B)/P(B) = 0.2/0.5 = 0.4)