In how many different ways can five students be seated in three chairs?
5 x 4 x 3 =60
am I right?
correct
In how many ways do 8 people sit on 3 chairs so that one of the seats is empty?
No, you are not right. The formula you used (5 x 4 x 3) is for finding the number of ways to arrange 3 items out of 5 without repetition, which is not the same as the number of ways to seat 5 students in 3 chairs.
To find the number of ways to seat 5 students in 3 chairs, we can use the concept of permutations. Since the order of seating matters (e.g., the first student to sit is different from the second student to sit), we can use a permutation formula.
The formula for finding the number of permutations is given by:
P(n, r) = n! / (n-r)!
Where:
- P(n, r) denotes the number of permutations of n items taken r at a time,
- n! represents the factorial of n, which is the product of all positive integers from 1 to n, and
- (n-r)! represents the factorial of (n-r).
In this case, we want to find the number of permutations when 5 students are seated in 3 chairs. Therefore, we have n = 5 (5 students) and r = 3 (3 chairs).
Using the permutation formula, we can calculate:
P(5, 3) = 5! / (5-3)!
= 5! / 2!
= (5 x 4 x 3 x 2 x 1) / (2 x 1)
= (120) / (2)
= 60.
Therefore, there are 60 different ways to seat five students in three chairs. So, your answer is correct.