How many subsets in all are there of a set containing 4 elements ?

Answer

To find the number of subsets of a set containing 4 elements, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Subsets**: A subset is any combination of elements from a set, including the empty set and the set itself.

2. **Identify the Number of Elements (n)**: In this case, the set contains 4 elements. So, we have \( n = 4 \).

3. **Use the Formula for the Number of Subsets**: The formula to calculate the number of subsets of a set is given by:
\[ \text{Number of subsets} = 2^n \]
where \( n \) is the number of elements in the set.

4. **Substitute the Value of n**: Since \( n = 4 \), we substitute this value into the formula:
\[ \text{Number of subsets} = 2^4 \]

5. **Calculate \( 2^4 \)**: Now, we calculate \( 2^4 \):
\[ 2^4 = 16 \]

6. **Conclusion**: Therefore, the total number of subsets of a set containing 4 elements is 16.

### Final Answer:
The number of subsets in all of a set containing 4 elements is **16**.

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