What is the total number of ways of selecting atleast one item from each of the two sets containing 6 identical items each?

Answer

To solve the problem of selecting at least one item from each of the two sets containing 6 identical items each, we can follow these steps:

### Step 1: Understand the Problem
We have two sets, S1 and S2, each containing 6 identical items. We need to select at least one item from each set.

### Step 2: Determine the Selection Options
For each set, since the items are identical, the number of ways to select items can be simplified. We can choose:
- 1 item
- 2 items
- 3 items
- 4 items
- 5 items
- 6 items

This gives us 6 possible choices for each set.

### Step 3: Calculate the Total Ways for Each Set
Since we need to select at least one item from each set, we can summarize the choices:
- For S1: 6 ways (choosing 1 to 6 items)
- For S2: 6 ways (choosing 1 to 6 items)

### Step 4: Combine the Choices
Since the selections from S1 and S2 are independent, we can multiply the number of ways to choose from each set:
\[ \text{Total Ways} = \text{Ways from S1} \times \text{Ways from S2} = 6 \times 6 = 36 \]

### Final Answer
Thus, the total number of ways of selecting at least one item from each of the two sets is **36**.

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