1. The problem is to understand and solve an "all ways" problem, which typically involves finding all possible ways to do something, often related to counting or combinatorics. 2. Since the problem statement is vague, let's consider a common example: "How many ways can you arrange $n$ distinct objects?" 3. The formula for the number of ways to arrange $n$ distinct objects is the factorial of $n$, denoted as $n!$. 4. Factorial is defined as $$n! = n \times (n-1) \times (n-2) \times \cdots \times 2 \times 1$$ 5. For example, if $n=4$, then $$4! = 4 \times 3 \times 2 \times 1 = 24$$ 6. This means there are 24 different ways to arrange 4 distinct objects. 7. If the problem involves choosing or arranging with repetition or restrictions, different formulas apply, but the factorial is the fundamental starting point. 8. To solve any "all ways" problem, identify the total number of items and the rules for arrangement or selection, then apply the appropriate counting principle. Final answer depends on the specific problem details, but factorial is the key concept for counting all ways to arrange distinct items.