How many ways can the offices of president, vice-president, treasurer, secretary, parliamentarian, and representative be filled from a class of 30 students?
combinations of 30, six at a time.
n!/[(r!)(n-r)!]
30*29*28*27*26*24 .../[(6*5*4*3*2)(24*23*....]
30*29*28*27*26 /(6*5*4*3*2)
30*29*28*27*26 / (30*4*3*2)
29*28*27*26 / (4*3*2)
29 * 7 * 9 * 13
To find the number of ways to fill the offices from a class of 30 students, we can use the concept of permutations.
First, let's find the number of possibilities for each office.
1. President: There are 30 students to choose from, so there are 30 possibilities for this office.
2. Vice-President: After selecting the president, there are 29 remaining students to choose from, resulting in 29 possibilities for this office.
3. Treasurer: After choosing the president and vice-president, there are 28 students remaining to choose from, resulting in 28 possibilities for this office.
4. Secretary: After selecting the president, vice-president, and treasurer, there are now 27 students left, resulting in 27 possibilities for this office.
5. Parliamentarian: After choosing the president, vice-president, treasurer, and secretary, there are 26 students remaining, resulting in 26 possibilities for this office.
6. Representative: Finally, after selecting the previous five positions, there are 25 students left, resulting in 25 possibilities for this office.
To find the total number of ways to fill all the offices, we multiply the number of possibilities for each office:
30 * 29 * 28 * 27 * 26 * 25 = 64,350,000
Therefore, there are 64,350,000 ways to fill the offices from a class of 30 students.