Five students are to be allocated into three distinguishable teams. . 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.
Five students are to be allocated into three distinguishable teams. . 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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:10. 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.
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.
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