The manager of a baseball team has 15 players to choose from for his 9 person batting order
2 answers:
Given the question:
The manager of a baseball team has 15 players to choose from for his 9-person batting order. How many different ways can he arrange the players in the lineup?
5,005 362,880 3,603,600 1,816,214,400
The number of was in which a smaller group is choosing from a bigger group is given by the bigger number combination the smaller number.
Here, we want to choose a 9-person batting order from a team of 15 players. This is given by:
The manager of a baseball team has 15 players to choose from for his 9-person batting order. How many different ways can he arrange the players in the lineup?
5,005 362,880 3,603,600 1,816,214,400
The number of was in which a smaller group is choosing from a bigger group is given by the bigger number combination the smaller number.
Here, we want to choose a 9-person batting order from a team of 15 players. This is given by:
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Answer:
c = 0.165
Step-by-step explanation:
Given:
f(x, y) = cx y(1 + y) for 0 ≤ x ≤ 3 and 0 ≤ y ≤ 3,
f(x, y) = 0 otherwise.
Required:
The value of c
To find the value of c, we make use of the property of a joint probability distribution function which states that
where a and b represent -infinity to +infinity (in other words, the bound of the distribution)
By substituting cx y(1 + y) for f(x, y) and replacing a and b with their respective values, we have
Since c is a constant, we can bring it out of the integral sign; to give us
Open the bracket
Integrate with respect to y
Substitute 0 and 3 for y
Add fraction
Rewrite;
The is a constant, so it can be removed from the integral sign to give
Integrate with respect to x
Substitute 0 and 3 for x
Multiply both sides by