There are 6 boys and 8 girls in a group of students. Calculate the number of ways that a president, vice-president and treasurer can be selected.
Please show your work.
14 students in all, no one student can occupy two posts.
Choose a president from 14 students, a vice-president from 13 remaining students, and a treasurer from the 12 remaining students.
There are six (3!) ways to "shuffle" the three posts, so
for a total of
14*13*12/3! = C(14,3) = 14!/((14-3)!3!)
ways
14 students in all, no one student can occupy two posts.
Choose a president from 14 students, a vice-president from 13 remaining students, and a treasurer from the 12 remaining students.
Number of ways to choose three distinct posts
=14*13*12
=14!/(14-3)!
thank you so much!
You're welcome!
To calculate the number of ways that a president, vice-president, and treasurer can be selected from a group of students, we can use the concept of permutations.
Since the positions of president, vice-president, and treasurer are distinct, we need to calculate the number of permutations for each position.
1. To choose the president, we have 14 students (6 boys + 8 girls) to choose from. So, there are 14 options for the president position.
2. After the president is chosen, we are left with 13 students to choose from for the vice-president position. Therefore, there are 13 options for the vice-president position.
3. Finally, after the president and vice-president are chosen, we have 12 students left to choose from for the treasurer position. Hence, there are 12 options for the treasurer position.
To calculate the total number of ways, we multiply the number of options for each position:
Total number of ways = 14 * 13 * 12 = 2,184
Therefore, there are 2,184 different ways that a president, vice-president, and treasurer can be selected from the group of students.