Final answer:
There are 720 permutations possible when selecting a sample of 3 from 10 people on a Caribbean cruise. This is calculated using the permutations formula, 10! / (10-3)!, which simplifies to 10 x 9 x 8.
Step-by-step explanation:
The student is asking about the number of permutations possible when selecting a sample of 3 people from a group of 10 on a Caribbean cruise. A permutation considers the order of selection to be important, which means that the arrangement of the selected people matters. To calculate permutations, you use the factorial function, which for a number n, is the product of all positive integers less than or equal to n.
To find the number of permutations (P) of selecting 3 people from a group of 10, you would calculate 10P3, which is the number of ways you can arrange 3 people out of 10. The formula for this is:
P(n, r) = n! / (n-r)!
Where P stands for permutations, n is the total number of items, and r is the number of items to choose. Plugging in our values we get:
P(10, 3) = 10! / (10-3)! = 10 x 9 x 8 = 720
Therefore, there are 720 permutations possible when selecting a sample of 3 from 10 people.