The question is there are 18 students in a class. Each day the teacher randomly selects three students to assist in a game: a leader, a recorder, and a timekeeper. In how many possible ways can the jobs be assigned?
so first is 1 out of 18
then since one was picked, now it is 1 out of 17
last, there is now 16, so 1 out of 16
now multiply 18x17x16=4896
Is this correct?
Thank you for checking my work
correct
No, that is not correct. The correct way to calculate the number of ways the jobs can be assigned is through a combination formula, rather than a multiplication.
To find the number of ways to select the leader, we start with 18 options. Once the leader is selected, there are 17 remaining students to choose from for the recorder. Finally, once the leader and recorder are selected, there are 16 remaining students for the role of timekeeper.
To calculate the total number of possible combinations, we multiply the number of options for each role:
18 options for the leader x 17 options for the recorder x 16 options for the timekeeper = 48,816
So, there are 48,816 possible ways the jobs can be assigned in this scenario.
Yes, your understanding and solution are correct. The number of ways in which the jobs can be assigned can be calculated by multiplying the number of choices for each position.
In the given scenario, for the first position (leader), there are 18 possible choices since there are 18 students in the class.
For the second position (recorder), once the leader is chosen, there are now 17 students left to choose from.
Similarly, for the third position (timekeeper), once the leader and recorder are chosen, there are 16 students left to choose from.
Therefore, the total number of possible ways to assign the jobs is calculated by multiplying these three numbers together: 18 * 17 * 16 = 4896.
Hence, your calculation of 4896 is correct. Well done!