The total number of selections of fruit which can be made from 3 bananas, 4 apples and 2 oranges, is

Options

A. 39
B. 315
C. 512
D. none of these

Answer

To solve the problem of finding the total number of selections of fruits that can be made from 3 bananas, 4 apples, and 2 oranges, we can break it down into steps:

### Step 1: Determine the number of ways to select bananas
We have 3 bananas. The number of ways to select bananas can be calculated as follows:
- We can select 0 bananas (1 way)
- We can select 1 banana (1 way)
- We can select 2 bananas (1 way)
- We can select 3 bananas (1 way)

Thus, the total number of ways to select bananas is:
\[ 0 + 1 + 1 + 1 = 4 \text{ ways} \]

### Step 2: Determine the number of ways to select apples
We have 4 apples. The number of ways to select apples is:
- We can select 0 apples (1 way)
- We can select 1 apple (1 way)
- We can select 2 apples (1 way)
- We can select 3 apples (1 way)
- We can select 4 apples (1 way)

Thus, the total number of ways to select apples is:
\[ 0 + 1 + 1 + 1 + 1 = 5 \text{ ways} \]

### Step 3: Determine the number of ways to select oranges
We have 2 oranges. The number of ways to select oranges is:
- We can select 0 oranges (1 way)
- We can select 1 orange (1 way)
- We can select 2 oranges (1 way)

Thus, the total number of ways to select oranges is:
\[ 0 + 1 + 1 + 1 = 3 \text{ ways} \]

### Step 4: Calculate the total number of selections
Now, we multiply the number of ways to select each type of fruit:
\[ \text{Total selections} = (\text{Ways to select bananas}) \times (\text{Ways to select apples}) \times (\text{Ways to select oranges}) \]
\[ \text{Total selections} = 4 \times 5 \times 3 = 60 \]

### Step 5: Subtract the case of selecting nothing
Since we are required to select at least one fruit, we need to subtract the case where no fruits are selected:
\[ \text{Total selections with at least one fruit} = 60 - 1 = 59 \]

### Final Answer:
The total number of selections of fruit which can be made from 3 bananas, 4 apples, and 2 oranges is **59**.

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