A fruit basket contains 4 oranges, 5 apples and 6 mangoes. The number of ways a person make selection of fruits from among the fruits in the basket is?

Answer

To find the number of ways a person can make a selection of fruits from the basket containing 4 oranges, 5 apples, and 6 mangoes, we can follow these steps:

### Step 1: Determine the number of choices for each type of fruit.
- For oranges, since there are 4 oranges, a person can choose from 0 to 4 oranges. This gives us:
- 0 oranges: 1 way
- 1 orange: 1 way
- 2 oranges: 1 way
- 3 oranges: 1 way
- 4 oranges: 1 way
- Therefore, the total number of ways to choose oranges is \(4 + 1 = 5\).

### Step 2: Determine the number of choices for apples.
- For apples, since there are 5 apples, a person can choose from 0 to 5 apples. This gives us:
- 0 apples: 1 way
- 1 apple: 1 way
- 2 apples: 1 way
- 3 apples: 1 way
- 4 apples: 1 way
- 5 apples: 1 way
- Therefore, the total number of ways to choose apples is \(5 + 1 = 6\).

### Step 3: Determine the number of choices for mangoes.
- For mangoes, since there are 6 mangoes, a person can choose from 0 to 6 mangoes. This gives us:
- 0 mangoes: 1 way
- 1 mango: 1 way
- 2 mangoes: 1 way
- 3 mangoes: 1 way
- 4 mangoes: 1 way
- 5 mangoes: 1 way
- 6 mangoes: 1 way
- Therefore, the total number of ways to choose mangoes is \(6 + 1 = 7\).

### Step 4: Calculate the total number of combinations.
- The total number of ways to select fruits from the basket is the product of the number of ways to choose each type of fruit:
\[ \text{Total ways} = (\text{Ways to choose oranges}) \times (\text{Ways to choose apples}) \times (\text{Ways to choose mangoes}) = 5 \times 6 \times 7 \]

### Step 5: Perform the multiplication.
- Now, calculate \(5 \times 6 = 30\).
- Then, calculate \(30 \times 7 = 210\).

### Step 6: Adjust for the case where no fruit is selected.
- The total number of ways calculated includes the case where no fruits are selected (0 oranges, 0 apples, and 0 mangoes). Since we want to exclude this case, we subtract 1 from the total:
\[ \text{Final answer} = 210 - 1 = 209 \]

### Final Answer:
The number of ways a person can make a selection of fruits from the basket is **209**.

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