Counting Billy's Coin Combinations & Gabriela's School Trip Time

AI Thread Summary
Billy has four coins (penny, nickel, dime, quarter) and needs to determine the number of ways to arrange them in four spaces, which involves calculating permutations. The solution involves multiplying the number of options for each space, resulting in 4! (4 factorial) or 24 combinations. For Gabriela's biking time, the problem assumes she travels the same distance as Juan, who takes 30 minutes to walk at a speed of 1/15 mile per minute. By calculating the distance Juan covers and dividing it by Gabriela's speed of 1/10 mile per minute, the time taken for her to bike to school can be determined. The discussion emphasizes the importance of understanding permutations and making reasonable assumptions about distances in word problems.
johnnyies
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Homework Statement


Billy has 1 penny, 1 nickel, 1 dime and 1 quarter. How many different ways can he put his coins in the following board by placing one coin in each cell?

Juan walks to school everyday. His walking speed is 1/15 mile per minute, and it takes him 30 minutes to get to school. His sister Gabriela bikes to school every day. Her biking speed is 1/10 mile per minute. How many minutes does it take Gabriela to get to school?

The Attempt at a Solution


Not sure how to do the first one. The second one I got the answer by multiplying Juan's speed x time to get the distance he traveled. Then with that distance, I divided it by Gabriela's speed to get how long it takes her. But the problem says nothing about the distances being the same, I just don't know
 
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I think you're right for the second question. The question implies the differences are the same because Gabriella and Juan probably live together and go to the same school! It's just an assumption you have to make ;)

For the first question, was there more to the problem statement? It says something about "the following board" but I see no board :)
 
oh, the first problem has a picture of a square divided into four squares, and you place a coin in each one. I don't remember how to do permutations (?) or combinations.
 
See if this helps: you can think of the 4 squares as being just four spaces. So arranging them in square form, you could arrange them _ _ _ _, and it works out the same. Does that make sense?

In this case you have a permutation, because the order that you put the coins down matters. So what do you think you should do? (Hint: how many ways can you fill the first space?)
 
it is rather easy, in the first task you need to multiply 4x3x2x1 then you will have all the possibilities, to next task i would suggest you to do it across , i mean 1/15 -- 30 and below 1/10 -- x , multiply across, and you have a right answer
good luck
 

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