Project ID:
7300000063
Accepted:
Type:
Layout:
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:
$${9\choose 3}=84$$
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:
$$9^3=729$$
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:
$$3\cdot 9=27$$
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:
$${3+3-1\choose 3} = 10$$
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:
$$\frac{9!}{6!}=9\cdot 8\cdot 7=504$$
Question 6:
Determine the number of ways to arrange in a row three blue, three orange, and three red cubes.
Answer 6:
$$\frac{9!}{3!\cdot3!\cdot3!}=1\,680$$