how many ways can 3 students be arranged in three chairs?
first chair: 3 choices
second chari:2 choices
third chair: 1 choice
what is 3*2*1?
if there the chairs are numbered
and students are a b and c
you can get
1 2 3
a b c
a c b
b a c
b c a
c a b
c b a
6 POSSIBLE WAYS
its denoted by 3!
WHICH IS = 3 x 2 x 1
you have a choice of 3 students for the first chair,
then of two students for the second chair and a choice of only one student for the third
To find the number of ways that 3 students can be arranged in 3 chairs, we can use the concept of permutations.
Permutations represent the different ways objects can be arranged or ordered. In this case, we want to find the number of permutations of 3 students in 3 chairs.
To solve this problem, we can use a simple formula for permutations:
P(n, r) = n! / (n - r)!
Where:
- P(n, r) represents the number of permutations of n objects taken r at a time.
- n! represents the factorial of n, which is the product of all positive integers from 1 to n.
In our case, n represents the total number of students (3), and r represents the number of chairs (also 3).
P(3, 3) = 3! / (3 - 3)!
= 3! / 0!
= 3! / 1
= 3 x 2 x 1 / 1
= 6
Therefore, there are 6 different ways that the 3 students can be arranged in the 3 chairs.