Question

there are 10 seats in an airport shuttle. how many ways can 6 people arrange themselves in the 10 seats?

Answer 1

To find out the number of ways 6 people can arrange themselves in 10 seats, we use permutations. The calculation is 10! / (10-6)! which equals 151,200 different arrangements.

Step-by-step explanation:

In mathematics, the question of how many ways 6 people can arrange themselves in 10 seats in an airport shuttle is an example of a permutation problem. Since there are more seats than people, and the order of seating matters, we can calculate the number of different arrangements using the permutation formula P(n, r) = n! / (n-r)!, where 'n' is the total number of seats, and 'r' is the number of people. Therefore, we calculate 10! / (10-6)! = 10! / 4! which simplifies to 10 × 9 × 8 × 7 × 6 × 5 = 151,200 ways that the 6 people can arrange themselves in the seats.

Answer 2

There are 210 different ways that 6 people can arrange themselves in the 10 seats of the airport shuttle.

Step-by-step explanation:

In this problem, we need to find the number of ways that 6 people can arrange themselves in 10 seats. This can be solved using combinations, which is a concept in combinatorics.

The formula for combinations is C(n, k) = n! / (k! * (n-k)!) where n is the total number of items and k is the number of items being chosen.

In this case, there are 10 seats and we need to choose 6 people to fill them. So, the formula becomes C(10, 6) = 10! / (6! * (10-6)!).

Simplifying the expression, we get C(10, 6) = 10! / (6! * 4!) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) = 210.

There are 210 different ways that 6 people can arrange themselves in the 10 seats of the airport shuttle.