Five A - list actresses are vying for the three leading roles in the new film `Catfight` in Denmark. The actress are Jullia Robards, Meryl Strep, Sally Fieldstone, Nicole Kadman, and Hallie Strawberry. Assuming that no actress has any advantage in getting any role, what is the probability that Julia and Hallie will star in the film together?

Answer

To solve the problem of finding the probability that Julia and Hallie will star in the film together, we can follow these steps:

### Step 1: Identify the total number of actresses and roles
We have 5 actresses: Julia Roberts (JR), Meryl Streep (MS), Sally Fieldstone (SF), Nicole Kidman (NK), and Hallie Strawberry (HS). There are 3 leading roles to fill.

### Step 2: Calculate the total ways to choose 3 actresses from 5
The total number of ways to choose 3 actresses from 5 can be calculated using the combination formula \( nCr \):

\[ 5C3 = \frac{5!}{3!(5-3)!} = \frac{5!}{3! \cdot 2!} = \frac{5 \times 4}{2 \times 1} = 10 \]

### Step 3: Calculate the favorable outcomes where Julia and Hallie are chosen
If Julia (JR) and Hallie (HS) are to be selected, we need to choose 1 more actress from the remaining 3 actresses (Meryl Streep, Sally Fieldstone, and Nicole Kidman).

The number of ways to choose 1 actress from these 3 is:

\[ 3C1 = \frac{3!}{1!(3-1)!} = \frac{3!}{1! \cdot 2!} = 3 \]

### Step 4: Calculate the total favorable outcomes
Since we have already determined that there are 3 ways to choose the third actress when Julia and Hallie are already chosen, the total number of favorable outcomes is 3.

### Step 5: Calculate the probability
The probability that Julia and Hallie will star in the film together is given by the ratio of the number of favorable outcomes to the total outcomes:

\[ P(\text{Julia and Hallie together}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{10} \]

### Final Answer
The probability that Julia and Hallie will star in the film together is \( \frac{3}{10} \).

---