Concept explainers
To calculate: The number of ways to form a 9-player team.
Answer to Problem 47E
The number of ways to form a 9-player teamare
Explanation of Solution
Given information:
There are 3 players for catcher, 4 players who can play first base, 6 players who can only pitch and for remaining 6 positions 14 players are there. A 9-player team is to be formed.
Formula used:
If there are n objects taken r at a time then combination is defined as
Calculation:
Consider the provided information that there are 3 players for catcher, 4 players who can play first base, 6 players who can only pitch and for remaining 6 positions 14 players are there. A 9-player team is to be formed.
In order to form a 9-player team, use combination as selection does not matter.
There are 3 ways to select a catcher, 4 ways to select a player who will play first base, 6 ways to select a player who can pitch.
Now, 3 positions out of 9 are filled to form a team.
Now, 14 players are available to fill 6 positions, so possible ways are
So, total number of required ways are
Recall that if there are n objects taken r at a time then combination is defined as
Here n is 14 and r is 6for
Thus, the number of ways to form a 9-player team are
Chapter 13 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
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