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How many ways are there to pick a group of n people from 100 people, and...
How many ways are there to pick a group of n people from 100 people, and...
How many ways are there to pick a group of n people from 100 people, and then pick a second group of m people from the remaining 100- n people, so that all the people you chose from the first group are taller than the people from the second group (assume that everyone in the group of 100 people has a different height) ote: it is implied in this question that 1 <n < 100 an d 0m100-n.
a. How many ways to pick president, secretary and treasurer from a group of 5 people?...
a. How many ways to pick president, secretary and treasurer from a group of 5 people? b. How many ways to get 3 heads, if you flip a coin 5 times (the order does not matter)?
In how many ways may n people sit around a round table? (Assume that when people...
In how many ways may n people sit around a round table? (Assume that when people are sitting around a round table, all that really matters is who is to each person’s right. For example, if we can get one arrangement of people around the table from another by having everyone get up and move to the right one place and sit back down, then we get an equivalent arrangement of people. Notice that you can get a list from...
Random variables and expected value Shared Birthday Height Arrangements Example: How many pairs of people in...
Random variables and expected value
Shared Birthday Height Arrangements Example: How many pairs of people in this room do we expect to share a birthday? Example: If we randomly arrange n people in a line, what is the expected number of people who are taller than all adjacent people? Assume each person's height is different (no ties). If there are 30 people in the room, how many pairs of people are there? What is the probability that two particular people...
Suppose we pick 2 integers together, in the range from 1 to 100. How many ways...
Suppose we pick 2 integers together, in the range from 1 to 100. How many ways are there to pick these 2 numbers such that their product is a multiple of 7? 5. How many even positive integers are there that are divisors of 30030? 6. Suppose 6 identical dice each with faces numbered 1 through 6 are tossed at the same time. What is the probability of the event "the result of the outcome is such that three different...
Suppose we pick 2 integers together, in the range from 1 to 100. How many ways...
Suppose we pick 2 integers together, in the range from 1 to 100. How many ways are there to pick these 2 numbers such that their product is a multiple of 7?
Please answer the following question: a) In how many ways can a committee of 3 people...
Please answer the following question:
a) In how many ways can a committee of 3 people be selected from a group of 10 people? b) In how many ways (different arrangements) can 8 books be placed on a shelf? c) On an ice cream menu, there are 5 choices of ice cream flavors, 4 choices of toppings and 2 choices of syrups. In how many different ways can the ice cream be ordered, if each order must include one ice...
Select a committee of 3 people from your staff of 9. How many different ways can...
Select a committee of 3 people from your staff of 9. How many different ways can this be accomplished? Select a committee of 3 people from your staff of 9. How many different ways can this be accomplished when one person will be the lead, one will be the record keeper, and one will be the researcher?
Question 17 3 pts In how many different ways can we seat three people with five...
Question 17 3 pts In how many different ways can we seat three people with five different chairs? O <=50 between 76 and 100 between 51 and 75 O > 500 O between 251 and 500 between 101 and 250
1. How many different ways can you have r numbers 1 sum up to a number...
1. How many different ways can you have r numbers 1 sum up to a number n? These are called compositions of a number n and it is easy to calculate from our understanding of binomial coefficients. So the number of compositions of 4 into 3 parts will be 1+1+2, 1+2+1, and 2+1+1. Note how we think of 1+1+2 and 1+2+1 as different-because in the first case, the first number is 1, second is 1 and third is 2, while...
How many ways are there to pick a group of n people from 100 people, and then pick a second group of m people from the remaining 100- n people, so that all the people you chose from the first group are taller than the people from the second group (assume that everyone in the group of 100 people has a different height) ote: it is implied in this question that 1 <n < 100 an d 0m100-n.
a. How many ways to pick president, secretary and treasurer from a group of 5 people? b. How many ways to get 3 heads, if you flip a coin 5 times (the order does not matter)?
Random variables and expected value
Shared Birthday Height Arrangements Example: How many pairs of people in this room do we expect to share a birthday? Example: If we randomly arrange n people in a line, what is the expected number of people who are taller than all adjacent people? Assume each person's height is different (no ties). If there are 30 people in the room, how many pairs of people are there? What is the probability that two particular people...
Suppose we pick 2 integers together, in the range from 1 to 100. How many ways are there to pick these 2 numbers such that their product is a multiple of 7? 5. How many even positive integers are there that are divisors of 30030? 6. Suppose 6 identical dice each with faces numbered 1 through 6 are tossed at the same time. What is the probability of the event "the result of the outcome is such that three different...
Please answer the following question:
a) In how many ways can a committee of 3 people be selected from a group of 10 people? b) In how many ways (different arrangements) can 8 books be placed on a shelf? c) On an ice cream menu, there are 5 choices of ice cream flavors, 4 choices of toppings and 2 choices of syrups. In how many different ways can the ice cream be ordered, if each order must include one ice...
Question 17 3 pts In how many different ways can we seat three people with five different chairs? O <=50 between 76 and 100 between 51 and 75 O > 500 O between 251 and 500 between 101 and 250
1. How many different ways can you have r numbers 1 sum up to a number n? These are called compositions of a number n and it is easy to calculate from our understanding of binomial coefficients. So the number of compositions of 4 into 3 parts will be 1+1+2, 1+2+1, and 2+1+1. Note how we think of 1+1+2 and 1+2+1 as different-because in the first case, the first number is 1, second is 1 and third is 2, while...
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