There are 12 students in a social studies class. Three students will be selected to present their term projects today. In how many different orders can three students be selected?
its A. 1,320
i just took the test
Answer - A. 1,320
That's not one of the answer choices.
A. 1,320
B. 220
C. 504
D. 36
urmom, do you have the rest of the ansvers by any chance ?
To find the number of different orders in which three students can be selected out of twelve, we can use the concept of permutations.
The formula for permutations is given by:
P(n, r) = n! / (n - r)!
Where:
P(n, r) represents the number of permutations of r items selected from a set of n items,
n! represents the factorial of n, which is the product of all positive integers from 1 to n.
In this case, we need to find the number of permutations of 3 students selected from a group of 12 students. Therefore, we can substitute n = 12 and r = 3 into the formula:
P(12, 3) = 12! / (12 - 3)!
= 12! / 9!
Now, let's calculate the value of 12! (12 factorial).
12! = 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
= 479,001,600
Next, let's calculate the value of 9! (9 factorial).
9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
= 362,880
Now we can substitute these values back into the permutation formula:
P(12, 3) = 479,001,600 / 362,880
= 1,320
Therefore, there are 1,320 different orders in which three students can be selected from a social studies class of twelve students.
Sorry - I missed the "three"
Ash
So is it a,b,c, or ,d?
Nope...
12 students and you are "choosing" three to do their presentation.
Order doesn't matter, so you have a combination 12C3
by definition of combination you have
12C3= n!/(r!(n-3)!
= 12! divided by 3!(9!)
= 12 x 11x10 /3x2x1
= ...