A particular American football play has eleven players: one quarterback, one running back, one center, two wide receivers, and six more offensive players. The coach calling the play has 3 quarterbacks, 2 running backs, 1 center, 4 wide receivers, and 20 other offensive players to choose from. When the play is called, the participating eleven players go onto the field to join the huddle in any order. Then, the play is lined up, where the participating players arrange themselves on the field in a particular way. (a) How many different possible combinations of players could there be in the huddle before the play is lined up? (b
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
A particular American football play has eleven players: one quarterback, one running back, one center, two wide receivers, and six more offensive players. The coach calling the play has 3 quarterbacks, 2 running backs, 1 center, 4 wide receivers, and 20 other offensive players to choose from. When the play is called, the participating eleven players go onto the field to join the huddle in any order. Then, the play is lined up, where the participating players arrange themselves on the field in a particular way.
(a) How many different possible combinations of players could there be in the huddle before the play is lined up?
(b) When the particular play is lined up, the offensive line is in the center of the field with three offensive players on each side of the center player (seven players total). The two wide receivers line up on opposite sides of the offensive line - one on the left, and one on the right. The quarterback is lined up behind the center, and the running back is lined up behind the quarterback. See the diagram below. How many different possible arrangements of players could there be to choose from given the choice of personnel already in the huddle?
W OOO C OOO W
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(c) When making the playbook, how many different ways are there for the coach to assign particular players to the final lineup positions for this play?
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