A lady wants to select one cotton saree and one polyester saree from a textile shop. If there are 10 cotton varieties and 12 polyester varieties, in how many ways can she choose the two sarees ?

Answer

To solve the problem of how many ways a lady can select one cotton saree and one polyester saree from a textile shop, we can follow these steps:

### Step-by-step Solution:

1. **Identify the number of choices for cotton sarees**:
The lady has 10 varieties of cotton sarees to choose from. Since she needs to select one, the number of ways to choose one cotton saree is given by the combination formula \( \binom{n}{r} \), where \( n \) is the total number of items to choose from and \( r \) is the number of items to choose. Here, it is \( \binom{10}{1} \).

\[ \text{Ways to choose cotton saree} = \binom{10}{1} = 10 \]

2. **Identify the number of choices for polyester sarees**:
The lady has 12 varieties of polyester sarees. Similarly, the number of ways to choose one polyester saree is \( \binom{12}{1} \).

\[ \text{Ways to choose polyester saree} = \binom{12}{1} = 12 \]

3. **Calculate the total number of combinations**:
Since the selection of cotton sarees and polyester sarees are independent events, we can multiply the number of ways to choose each type of saree to find the total number of combinations.

\[ \text{Total ways to choose sarees} = \text{Ways to choose cotton saree} \times \text{Ways to choose polyester saree} = 10 \times 12 \]

\[ \text{Total ways to choose sarees} = 120 \]

### Final Answer:
The lady can choose the two sarees in **120 different ways**.

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