The first question I have the answer.The second question is: explain how this compares with 20C5 and 20P5. **Calculating Combinations: Step-by-Step Process**To find the number of ways to choose a subset of subjects from a larger group, use combinations and factorials. Here's a walkthrough of the process:1. **Identify the Total Number of Subjects and Selection Size:** - You have 20 subjects and want to select 5. 2. **Set up the Basic Combination Formula:** - Use the formula \(\frac{n!}{(n-r)!}\) where \(n\) is the total number of subjects (20) and \(r\) is the number of subjects you want to select (5). - This becomes \(\frac{20!}{(20-5)!}\).3. **Simplify the Factorial Expression:** - \(20! = 20 \times 19 \times 18 \times 17 \times 16 \times 15!\) - \((20-5)! = 15!\)4. **Expand and Simplify:** - Write the expanded form: \(20 \times 19 \times 18 \times 17 \times 16 \times 15!\) - Since \(15!\) appears in both the numerator and denominator, you can cancel it out.5. **Perform the Multiplication:** - Calculate \(20 \times 19 \times 18 \times 17 \times 16 = 1,860,480\). - This is the number of ways to select 5 subjects out of 20.6. **Result:** - The final answer is 1,860,480.This approach illustrates the simplification of factorial expressions in combinations using cancellation, resulting in an easier computation.

Permutation: It is the arrangement of items, which the items are arrange order. So we say that permutation is order matter.Combination: It is a selection of items in which the order does not matter nPr = n! / (n-r)!nCr = n! / (r!(n-r)!)The relationship between the permutation and combinations is givennPr = r! nCr