Question

1. donations emily has 20 collectible dolls from different countries that she will donate. if she selects 10 of them at random, what is the probability that she chooses the dolls from ecuador, paraguay, chile, france, spain, sweden, switzerland, germany, greece, and italy?

Explanation:

Step1: Identify the total number of ways to choose 10 dolls from 20.

This is a combination problem. The formula for combinations is \( C(n, k) = \frac{n!}{k!(n - k)!} \), where \( n = 20 \) and \( k = 10 \). So the total number of ways to choose 10 dolls from 20 is \( C(20, 10) \).

Step2: Identify the number of favorable outcomes.

There is only 1 way to choose the specific 10 dolls (from Ecuador, Paraguay, Chile, France, Spain, Sweden, Switzerland, Germany, Greece, and Italy).

Step3: Calculate the probability.

Probability \( P \) is the number of favorable outcomes divided by the total number of outcomes. So \( P = \frac{1}{C(20, 10)} \).

First, calculate \( C(20, 10) = \frac{20!}{10!(20 - 10)!} = \frac{20!}{10!10!} = 184756 \).

So the probability is \( \frac{1}{184756} \).

Answer:

\(\frac{1}{184756}\)