Word Problems II

Submitted by vladimir.arzt on Wed, 08/28/2024 - 11:36
Project ID: 
7300000063
Accepted: 
SubArea: 
Combinatorics
Type: 
Scrolling
Layout: 
6x6
Question: 
Match each description of a combinatorial problem to its corresponding solution.
Questions Title: 
Combinatorial Problem
Answers Title: 
Solution
Question 1: 
Determine the number of possible passwords to open a lock, given that entering the password involves pressing three of the buttons labeled 1-9 (the buttons remain pressed after being pushed).
Answer 1: 
(93)=84
Question 2: 
Determine the number of possible passwords to open a lock, given that entering the password involves entering a three-digit numeric code using the buttons labeled 1-9 (the buttons can be pressed repeatedly).
Answer 2: 
93=729
Question 3: 
Determine the number of possible outfits if an outfit consists of jeans and a T-shirt, given that you have three different types of jeans and nine T-shirts of different colors.
Answer 3: 
3⋅9=27
Question 4: 
Determine the number of ways to choose 3 cakes from a selection of 4 poppy seed cakes, 3 cottage cheese cakes, and 5 walnut cakes.
Answer 4: 
(3+3−13)=10
Question 5: 
Determine the number of ways to create a candle with three horizontal stripes using different colored waxes (there are 9 colors of wax to choose from).
Answer 5: 

9!6!=9⋅8⋅7=504

Question 6: 
Determine the number of ways to arrange in a row three blue, three orange, and three red cubes.
Answer 6: 
9!3!⋅3!⋅3!=1680