***MULTINOMIAL COEFFICIENTS*** Really just need help understanding this better having trouble getting the right answer. Five students are to be allocated into three distinguishable teams. A) How many distributions are there? In other words how many different possible sizes can the teams have? (Include empty teams.) e.g. “Team 1 and 2 each have two members and Team 3 has one member” is one of the distributions being counted; perhaps 221 is a good way to represent this distribution. Enumerate (list out) all possible distributions and then check your answer with the appropriate formula. 1.B) Suppose a distribution is chosen: two students will be on the first and second teams each, while a single student will be on the third team. How many different combinations of teams are there? e.g. “Team 1: Alicia and Carlos, Team 2: Davina and Bob, Team 3: Erik” is one of the combinations of teams being counted. Perhaps AC|DB|E is a good way to represent these teams. Enumerate all possible combinations of teams and check your answer with the appropriate formula. 2. What is the coefficient of the term w^3x^4yz in the polynomial (w+x+y+z)^9?
***MULTINOMIAL COEFFICIENTS***
Really just need help understanding this better having trouble getting the right answer.
Five students are to be allocated into three distinguishable teams.
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A) How many distributions are there? In other words how many different possible sizes can the teams have? (Include empty teams.) e.g. “Team 1 and 2 each have two members and Team 3 has one member” is one of the distributions being counted; perhaps 221 is a good way to represent this distribution. Enumerate (list out) all possible distributions and then check your answer with the appropriate formula.
1.B) Suppose a distribution is chosen: two students will be on the first and second teams each, while a single student will be on the third team. How many different combinations of teams are there? e.g. “Team 1: Alicia and Carlos, Team 2: Davina and Bob, Team 3: Erik” is one of the combinations of teams being counted. Perhaps AC|DB|E is a good way to represent these teams. Enumerate all possible combinations of teams and check your answer with the appropriate formula.
2. What is the coefficient of the term w^3x^4yz in the polynomial (w+x+y+z)^9?
"Since you have asked multiple questions, we will solve the first question for you. If you want any specific question to be solved then please specify the question number post only that question"
The formula to calculate the number of combination is
Where, number of object
number of objects being chosen at a time.
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