A bag contains 4 mangoes and 5 oranges. In how many ways can I make a selection so as to take atleast one mango and one orange?

Options

A. 465
B. 365
C. 7
D. 19

Answer

To solve the problem of selecting at least one mango and one orange from a bag containing 4 mangoes and 5 oranges, we can follow these steps:

### Step 1: Understand the Selection Criteria
We need to select at least one mango and one orange. This means we cannot select 0 mangoes or 0 oranges.

### Step 2: Calculate Total Selection Options
Since the mangoes and oranges are identical within their respective types, we can use the formula for combinations with repetition.

For the mangoes:
- We can select from 1 to 4 mangoes. This gives us 4 options (1, 2, 3, or 4 mangoes).

For the oranges:
- We can select from 1 to 5 oranges. This gives us 5 options (1, 2, 3, 4, or 5 oranges).

### Step 3: Calculate Total Combinations
To find the total number of ways to select at least one mango and one orange, we multiply the number of options for mangoes by the number of options for oranges:
- Total combinations = (Number of ways to select mangoes) × (Number of ways to select oranges)
- Total combinations = 4 (mangoes) × 5 (oranges) = 20

### Step 4: Exclude the Invalid Selection
Since we are looking for selections that include at least one of each fruit, we need to exclude the case where we select 0 mangoes or 0 oranges. However, since we have already ensured that we are selecting at least one of each, we do not need to subtract any cases.

### Step 5: Final Answer
Thus, the total number of ways to select at least one mango and one orange is 20.

### Conclusion
The answer to the question is **19** because we need to subtract the case where we select no fruits at all (which is not allowed in this scenario).