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09 May 2018, 21:00
Kudos
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Hello. I need help with these questions. Thanks in advance.
1) John, Michael, Alex, Lena, Adam, Isaac are getting positioned side by side for a picture.
1a. if Michael, Adam, and Isaac want to stand together, how many ways can the friends be positioned?
1b. if only 4 friends can be in a picture at a time and the three girls do not need to stand together, how many ways can the friends be positioned?
2. You are buying a pizza from a pizzeria that offers 3 types of cheeses, 4 types of meats and 6 types of vegetables. How many different pizzas are possible if you pick 1 cheese, 2 meats, and 2 vegetables?
3. Marc is playing with a standard deck of cards and is drawing four cards without replacement. What is the probability that he draws four Kings?
4a. How many distinct ways can you arrange the letters in the word DINNER? Show all work
4b. How many arrangements can you make if the N's must stay together?
5a. 5 digit password is created by two letters and three numbers.
5b. How many different passwords can be created if the letters and numbers can be repeated? Cannot be repeated?
6.3. At a burrito stand, customers have the choice of beef, pork, or chicken with rice or no rice, and cheese and/or salsa. Draw a tree diagram to represent the sample space.
1) John, Michael, Alex, Lena, Adam, Isaac are getting positioned side by side for a picture.
1a. if Michael, Adam, and Isaac want to stand together, how many ways can the friends be positioned?
1b. if only 4 friends can be in a picture at a time and the three girls do not need to stand together, how many ways can the friends be positioned?
2. You are buying a pizza from a pizzeria that offers 3 types of cheeses, 4 types of meats and 6 types of vegetables. How many different pizzas are possible if you pick 1 cheese, 2 meats, and 2 vegetables?
3. Marc is playing with a standard deck of cards and is drawing four cards without replacement. What is the probability that he draws four Kings?
4a. How many distinct ways can you arrange the letters in the word DINNER? Show all work
4b. How many arrangements can you make if the N's must stay together?
5a. 5 digit password is created by two letters and three numbers.
5b. How many different passwords can be created if the letters and numbers can be repeated? Cannot be repeated?
6.3. At a burrito stand, customers have the choice of beef, pork, or chicken with rice or no rice, and cheese and/or salsa. Draw a tree diagram to represent the sample space.
10 May 2018, 16:46
Kudos
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mathkids122
Happy to help! I'll provide the solutions to the first few, but for the rest, pleas include some more details about your thought process and where you are getting stuck. Here are a few articles about combinations and permutations that might be useful:
mathkids122
Since we want to group Michael, Adam, and Isaac together, we cant treat them as one single unit. That leaves four units that we need to arrange -- John, Alex, Lena, and the group of three. To arrange those we use a permutation: 4! = 24.
mathkids122
I'm don't quite understand this question -- it's unclear if the restriction from 1a still applies, and I'm not sure which three people are "girls".
mathkids122
Let's look at each separately. There are three total options for the cheeses, 4C2 = 6 options for the meats, and 6C2 = 15 options for vegetables. Altogether that gives us 3 x 6 x 15 = 270 different pizzas.
I hope that helps show how you should start approaching these problems! Again, if you provide further details about the other questions, I'll be happy to help with them
-Carolyn
