Week 10 Essay
WEEK 10:
TITLE: BINOMIAL THEOREM, COUNTING PRINCIPLE, PERMUTATION, AND COMBINATION
Christina Bryant
Define Binomial Coefficient. Give an example. Write the steps of a Graphing Utility to evaluate your Binomial Coefficient and the final answer.
Binomial coefficients are a family of positive integers that occurs as coefficients in the binomial theorem.
(10¦10)
(10¦10)=10!/(10-10)!10!
=10!/0!10!
=10!/(1)(10!)
=10!/10!
=1
Final answer is 1. Explain the fundamental counting principle in two to three sentences. Give an example.
The principle states that if a sequence of m outcomes can occur in such a way that the first outcome can occur in n1 ways, the second can occur in nm ways, then the number of ways that is sequence can result …show more content…
The menu says pancakes, waffles, or home fries. And to drink, coffee, juice, hot chocolate, and tea. How many different choices of food and drink do you have?
The 3 choices for food and 4 choices for drink; thus, I have a total of 3*4= 12 choices State the difference between permutation and combination.
The difference is that if the order doesn’t matter, it’s a combination and if the order does matter it is a permutation.
4. There are 14 performers who will present their comedy acts this weekend at a comedy club. One of the performers insists on being the last stand-up comic of the evening, and one of the performers wants to be the first. If these performer’s requests are granted, how many different ways are there to schedule the appearances? (14-2)! = 479001600
Of the 100 people in the U.S. Senate, 18 serve on the Foreign Relations Committee. How many ways are there to select Senate members for this committee (assuming party affiliation is not a factor in selection)? 100c18=100!/[(100-18)!*18!]=30,664,510,802,988,208,300
6. A fair coin is tossed two times in succession. The set of equally likely outcomes is {HH, HT, TH, TT}. Find the probability of getting exactly two
TITLE: BINOMIAL THEOREM, COUNTING PRINCIPLE, PERMUTATION, AND COMBINATION
Christina Bryant
Define Binomial Coefficient. Give an example. Write the steps of a Graphing Utility to evaluate your Binomial Coefficient and the final answer.
Binomial coefficients are a family of positive integers that occurs as coefficients in the binomial theorem.
(10¦10)
(10¦10)=10!/(10-10)!10!
=10!/0!10!
=10!/(1)(10!)
=10!/10!
=1
Final answer is 1. Explain the fundamental counting principle in two to three sentences. Give an example.
The principle states that if a sequence of m outcomes can occur in such a way that the first outcome can occur in n1 ways, the second can occur in nm ways, then the number of ways that is sequence can result …show more content…
The menu says pancakes, waffles, or home fries. And to drink, coffee, juice, hot chocolate, and tea. How many different choices of food and drink do you have?
The 3 choices for food and 4 choices for drink; thus, I have a total of 3*4= 12 choices State the difference between permutation and combination.
The difference is that if the order doesn’t matter, it’s a combination and if the order does matter it is a permutation.
4. There are 14 performers who will present their comedy acts this weekend at a comedy club. One of the performers insists on being the last stand-up comic of the evening, and one of the performers wants to be the first. If these performer’s requests are granted, how many different ways are there to schedule the appearances? (14-2)! = 479001600
Of the 100 people in the U.S. Senate, 18 serve on the Foreign Relations Committee. How many ways are there to select Senate members for this committee (assuming party affiliation is not a factor in selection)? 100c18=100!/[(100-18)!*18!]=30,664,510,802,988,208,300
6. A fair coin is tossed two times in succession. The set of equally likely outcomes is {HH, HT, TH, TT}. Find the probability of getting exactly two