Counting Principle
Flashcard
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Hard
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the Counting Principle in combinatorics?
Back
The Counting Principle states that if there are 'm' ways to do one thing and 'n' ways to do another, then there are m × n ways to do both.
2.
FLASHCARD QUESTION
Front
How many different lunches can be made if a student can choose one sandwich, one salad, and one piece of fruit from given options?
Back
To find the total combinations, multiply the number of choices for each category: 3 sandwiches × 2 salads × 3 fruits = 18 different lunches.
3.
FLASHCARD QUESTION
Front
What is the formula to calculate the number of ways to choose 'r' items from 'n' items without regard to the order?
Back
The formula is given by the binomial coefficient: C(n, r) = n! / (r!(n-r)!) where '!' denotes factorial.
4.
FLASHCARD QUESTION
Front
If there are 9 types of ice cream and 4 friends, how do you calculate the probability that each friend orders a different type?
Back
Calculate the total arrangements of 9 types taken 4 at a time (P(9, 4)) and divide by the total possible orders (9^4). The probability is 336/729.
Tags
CCSS.HSS.CP.B.9
5.
FLASHCARD QUESTION
Front
How many different Personal Identification Numbers (PINs) can be created with 2 letters followed by 2 digits if repetition is allowed?
Back
The number of PINs is calculated as: 26^2 (for letters) × 10^2 (for digits) = 67600.
6.
FLASHCARD QUESTION
Front
What is the total number of possible 4-digit PIN codes?
Back
Each digit can be any number from 0 to 9, so the total is 10^4 = 10,000 possible PIN codes.
7.
FLASHCARD QUESTION
Front
How many ways can a quiz with 3 true/false questions be completed?
Back
Each question has 2 possible answers (true or false), so the total ways to complete the quiz is 2^3 = 8.
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