A has:

1 subset with zero elements = ∅

4 subsets with one element = {a}, {b}, {c} and {d}

6 subsets with two elements = {a, b}, {a, c}, {a, d}, {b, c}, {b, d} and {c, d}

4 subsets with three elements = {a, b, c}, {a, b, d}, {a, c, d} and {b, c, d}

1 subset with four elements = {a, b, c, d}

Therefore A has 16 subsets altogether.

**Note:**

1. Remember that order doesn't matter. So, for example, {a, b} and {b, a} are the same subset.

2. The numbers 1, 4, 6, 4 and 1 are Binomial coefficients and occur in the fifth row of Pascal's triangle.

3. 16 = 2^{4}. Generally a set with n elements has 2^{n} subsets.

I found an answer from www.quora.com

If A= {a, **b**,**c**, **d**}, then how **many subsets does the set A have**? - Quora

The number of **subsets** of a **set** is 2^n, where n is the cardinality of the **set**. **D has** 4 elements. So it **has** 2^4 = 16 **subsets**, including The Empty **Set** and **D** itself.

For more information, see If A= {a, **b**,**c**, **d**}, then how **many subsets does the set A have**? - Quora

I found an answer from en.wikipedia.org

Power **set** - Wikipedia

In mathematics, the power **set** (or powerset) of a **set** S is the **set** of all **subsets** of S , including the ... For example, the power **set** of a **set** with three elements, **has**: ... the singleton **subsets**),; **C**(3, 3) = 1 **subset** with 3 elements (the original **set** itself). ... However, there are two important properties of **subsets** that **do** not carry over to ...

For more information, see Power **set** - Wikipedia