From 2 mangoes, 3 oranges and 4 apples, how many selections of fruits can be made by taking :
(i) at least one of them
(ii) at least one of each kind ?

Answer

To solve the problem, we will break it down into two parts as specified in the question.

### Part (i): Selections of fruits with at least one of them

1. **Identify the number of options for each type of fruit:**
- For mangoes: We can choose 0, 1, or 2 mangoes. This gives us 3 options (0, 1, 2).
- For oranges: We can choose 0, 1, 2, or 3 oranges. This gives us 4 options (0, 1, 2, 3).
- For apples: We can choose 0, 1, 2, 3, or 4 apples. This gives us 5 options (0, 1, 2, 3, 4).

2. **Calculate the total selections including the option of choosing none:**
- Total selections = (number of options for mangoes) × (number of options for oranges) × (number of options for apples)
- Total selections = 3 × 4 × 5 = 60.

3. **Subtract the case where no fruit is selected:**
- Since we need at least one fruit, we subtract the case where we select 0 mangoes, 0 oranges, and 0 apples (which is 1 case).
- Therefore, the total selections with at least one fruit = 60 - 1 = 59.

### Part (ii): Selections of fruits with at least one of each kind

1. **Identify the number of options for each type of fruit, ensuring at least one of each is selected:**
- For mangoes: We can choose either 1 or 2 mangoes. This gives us 2 options (1, 2).
- For oranges: We can choose either 1, 2, or 3 oranges. This gives us 3 options (1, 2, 3).
- For apples: We can choose either 1, 2, 3, or 4 apples. This gives us 4 options (1, 2, 3, 4).

2. **Calculate the total selections ensuring at least one of each type:**
- Total selections = (number of options for mangoes) × (number of options for oranges) × (number of options for apples)
- Total selections = 2 × 3 × 4 = 24.

### Final Answers:
- (i) The number of selections of fruits with at least one of them is **59**.
- (ii) The number of selections of fruits with at least one of each kind is **24**.