Nine people on a baseball team are trying to decide who will play which position.

a. in how many different ways could they select a person to be pitcher?

b. after someone has already been selected as pitcher, how mandy different ways could they select someone else to be catcher?

c. in how many different ways could they select a pitcher and a catcher?

d. after the pitcher and catcher have been slected, in ohw many ways could they select a first baseman?

e. in how many different ways could they sleect a pitcher, a catcher , and af irst baseman?

f. In how many different ways could all nine positions be filled?

my answers:
a.9
b.8
c.81
d.6
e.729
f.9

are those right?? please help

c is wrong, the answer is 9x8=72

d is wrong, the answer is 7
e is wrong, the answer is 9x8x7=504
f is wrong, the answer is 9! or 9 factorial, or 9x8x7x6x5x4xx3x2x1 =362,880

yessir

Let's break down each question and explain how to get the correct answers:

a. In how many different ways could they select a person to be pitcher?
Since there are 9 people on the team, there are 9 different options for the pitcher position. Therefore, your answer of 9 is correct.

b. After someone has already been selected as pitcher, how many different ways could they select someone else to be catcher?
Since the pitcher position has already been filled, there are now 8 remaining players to choose from for the catcher position. Hence, the correct answer is 8.

c. In how many different ways could they select a pitcher and a catcher?
To find the total number of ways to select a pitcher and a catcher, you multiply the number of options for each position. As you correctly found that there are 9 options for a pitcher and 8 options for a catcher, the answer would be 9 multiplied by 8, which equals 72. Therefore, the correct answer is 72.

d. After the pitcher and catcher have been selected, in how many ways could they select a first baseman?
After the pitcher and catcher are chosen, there are still 7 remaining players to choose from for the first baseman position. Thus, the correct answer is 7.

e. In how many different ways could they select a pitcher, a catcher, and a first baseman?
To find the total number of ways to select these three positions, you need to multiply the number of options for each position. As you correctly calculated that there are 9 options for a pitcher, 8 options for a catcher, and 7 options for a first baseman, the answer would be 9 multiplied by 8 multiplied by 7, which equals 504. Therefore, the correct answer is 504.

f. In how many different ways could all nine positions be filled?
To calculate this, you multiply the number of options for each position together. Continuing from the previous question, we have determined that there are 504 ways to select the pitcher, catcher, and first baseman. After selecting those three positions, there are 6 remaining players to choose from for the next position, then 5 for the following position, and so on. Therefore, the answer would be 504 multiplied by 6 multiplied by 5 multiplied by 4 multiplied by 3 multiplied by 2, which equals 86,400. Hence, the correct answer is 86,400.

In summary, the correct answers are:
a. 9
b. 8
c. 72
d. 7
e. 504
f. 86,400

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