Question

natalie can take one of her three friends with her on a trip to italy. she cant decide whom to take. nick suggests that natalie use a random number generator to assign numbers 1 through 20 to him, sarah, and mike until all the numbers are used. then natalie can pick a number from 1 to 20, and that friend will go. is nicks suggestion fair? explain.
no, one friend will have fewer numbers assigned.
no, two friends will have fewer numbers assigned.
yes, each friend is assigned the same amount.

Explanation:

Step1: Calculate the number of numbers each friend should get if fair

If we divide 20 numbers among 3 friends, \(20\div3 = 6\frac{2}{3}\). Since the number of assigned numbers must be an integer, we check the remainder.

Step2: Analyze the assignment

When we assign numbers 1 - 20 to 3 friends, \(20 = 3\times6+2\). So two friends will get 6 numbers and one friend will get \(6 + 2=8\) numbers.

Answer:

No, one friend will have fewer numbers assigned.