there are 10 students in a social studies class. three students will be selected to present their term projects today. In how many different orders canthree students be selected?

combinations of 10 three at a time

=
10!/ [ 3! (10-3)! ]

= 10 * 9 * 8 *7* .......1 /[3*2(7*....1) ]

= 10 * 3 * 4

= 120

or look up binary coefficient (10,3)
= 120

or look at Pascal's triangle row 10, element 3 (the eleventh row, fourth element really since zero counts) again 120

thank you so much

Well, let me calculate that for you. To choose the first student, you have 10 options. After selecting the first student, you have 9 options left for the second student. Finally, for the last student, you have 8 options.

To find the total number of different orders, we multiply the number of options for each student together: 10 * 9 * 8 = 720.

So, there are 720 different orders in which three students can be selected. That's a lot of possibilities! They'll have to practice their presentations. Good luck to them!

To determine the number of different orders in which three students can be selected out of a class of ten students, we can use the concept of combinations.

The combination formula is given by:

C(n, r) = n! / (r!(n-r)!)

Where:
- n is the total number of items to choose from (in this case, the total number of students)
- r is the number of items to be chosen (in this case, the number of students to be selected)
- ! denotes the factorial operation

Using the combination formula:

C(10, 3) = 10! / (3!(10-3)!) = 10! / (3!7!)

Simplifying further:

C(10, 3) = (10 * 9 * 8 * 7!) / (3 * 2 * 1 * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120

Hence, there are 120 different orders in which three students can be selected from a class of ten students.

To calculate the number of different orders in which the three students can be selected, we can use the concept of permutations.

The formula to calculate permutations is:

P(n, r) = n! / (n - r)!

Where n is the total number of items and r is the number of items selected.

In this case, we have 10 students (n) and we need to select 3 students (r).

So, using the formula:
P(10, 3) = 10! / (10 - 3)!

10! means 10 factorial, which is the product of all positive integers from 1 to 10.

(10 - 3)! means factorial of (10 - 3), which is factorial of 7.

Simplifying the formula:
P(10, 3) = 10! / 7!

10! = 10 * 9 * 8 * 7!

So, our formula becomes:
P(10, 3) = (10 * 9 * 8 * 7!) / 7!

The 7! in the numerator and denominator cancel each other out.

P(10, 3) = 10 * 9 * 8

Calculating the remaining expression:
P(10, 3) = 720

Therefore, there are 720 different orders in which the three students can be selected.