roll the dice so that it is guaranteed that there exists some face that shows up at least 8 times?3. Consider rolling a dice with 6 faces. What is the minimum number of times you have to the4. How many different ways are there to pick 4 students from a group of 10 students to form ateam?5. How many strings of length 6 decimal digits are thorodigit is andigithe last

What is the minimum number of times you 4. How many different ways are there to pick 4 students from a group of 10 students to form a the dice so that it is guaranteed that there exists some face that shows up at least 8 times? team? 5. How

What is the minimum number of times you 4. How many different ways are there to pick 4 students from a group of 10 students to form a the dice so that it is guaranteed that there exists some face that shows up at least 8 times? team? 5. How

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Nine IU South Bend students are going on a trip to Indianapolis for a Clots game. Go Colts! (a) They will seat in a row. In how many ways can they seat if Josh, Mark and Mary will sit together? (b) They will travel with three cars that hold 2, 4, and 5 people, respectively. All of them can drive. Find the number of possible ways to allocate 9 people to 3 cars that each car has at least one person (each car has to have a driver) (i) if the allocations are to the cars only (disregard the seats in the car). (ii) if the allocations are to the seats.
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What is the prabability if I roll a dice once and get: a.the face is odd or a three? b.given that the face is odd, it is a one? I know for a, odd number and 3 are non-exclusive so P(odd U 3) supposed to be P(odd)+P(3)-P(odd n 3)=7/12 but this is not the right answer, why?
Suppose you are playing a game of Yahtzee. You know that you play with 5 dice, each with 6 sides. Since the dice are all rolled at the same time, let the roll (5, 4, 3, 2, 1) to be equal to (2, 4, 5, 1, 3). Assume for this question that we will only be rolling the dice once. (i) How many ways can you roll all the dice? (ii) To win 50 points you would need all the dice to roll the same number (ex. (1, 1, 1, 1, 1)). How many ways can you win the 50 points? (iii) Suppose you are trying to get your dice to roll only consecutive numbers (ex. (1, 2, 3, 4, 5) or (2, 3, 4, 5, 6)) How many different ways are there to do this? (iv) Suppose instead you are trying to get your dice to roll 4 consecutive numbers (ex. (1, 2, 3, 4, 1) or (2, 3, 4, 5, 3)) How many different ways are there to do this? (make sure to not count any only consecutive numbers) This is a combinatorics math counting problem.
List all the possible outcomes from flipping a coin twice and spinning a spinner with three sections labeled red, yellow, and blue. {HHr, HHy, HHb, HTr, HTy, HTb, THr, THy, THb, TTr, TTy, TTb} {HH1, HH2, HH3, HH4, HT1, HT2, HT3, HT4, TH1, TH2, TH3, TH4T, TT1, TT2, TT3, TT4} {HHr, HHy, HHb, HTr, HTy, HTb, THr, THy, THb} {HH1, HH2, HH3, HT1, HT2, HT3, TH1, TH2, TH3, TT1, TT2, TT3}
A bagel shop has a selection of 8 different kinds of bagels (at least 10 of each). (.1) How many different selections of 10 bagels can be made? ( .2) If garlic is one kind of available bagel and onion is another, how many different selections of 10 bagels can you make so that you have at least 3 onion bagels and exactly 2 garlic bagels?
A: Green is just as likely as red or blue to appear. B: Green is just as likely as blue to appear, but not as likely as red. C: Green is not as likely as red or blue to appear. D: Green is not as likely as blue to appear, but is as likely as red.
I need help on both questions. Thank you in advance!
Discrete Math. I just need help understanding the set up. Part A is 100 ways and Part B is 30,240
Suppose that nine children are sitting in a row. When the music starts, they get up and run around the row of chairs. When the music stops they each sit in an empty chair. In how many ways can it happen that none of them are sitting in the original chair that they occupied at the start of the game? Use an approximation for your answer and round it to the nearest whole number.