In a geography class 9 students are scheduled to give their presentations tody, one student must leave early so he will present first, how many different ways can you schedule all of todays presentations?
one student's position is fixed .now the remaining 8 students can give their presentations in 8! ways
8!=8*7*6*5*4*3*2*1=40320
To find the number of different ways to schedule all of today's presentations, we need to consider that one student must present first. Let's solve this step-by-step:
Step 1: Select one student to present first.
There are 9 students to choose from, so there are 9 choices for the first presenter.
Step 2: Arrange the remaining 8 students.
After the first presenter, there are 8 students remaining to give their presentations. We need to arrange them in a specific order.
The number of ways to arrange these students in order is given by 8 factorial (8!).
Step 3: Multiply the results from Step 1 and Step 2.
Now, we multiply the number of choices for the first presenter (9) by the number of ways to arrange the remaining students (8!):
9 * 8! = 9 * (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)
= 9 * 40,320
= 362,880
Therefore, there are 362,880 different ways to schedule all of today's presentations, given that one student must present first.
To solve this problem, we can use the concept of permutations. Since one student must leave early and present first, we can consider this student as fixed in the first position.
Now, we have 8 remaining students who need to present. The order in which they present matters, so we need to calculate the number of permutations of these 8 students.
The number of permutations can be calculated using the formula for permutations of n items taken r at a time, which is given by:
P(n, r) = n! / (n - r)!
In this case, n = 8 (as we have 8 students remaining) and r = 8 (since we need to arrange all the students).
Using this formula, we can calculate the number of permutations:
P(8, 8) = 8! / (8 - 8)!
= 8! / 0!
= 8! / 1
= 8!
Therefore, there are 8! (8 factorial) different ways to schedule all the presentations in today's geography class.