Find the number of combinations that can be formed with 5 oranges, 4 mangoes and 3 bananas, when one fruit of each kind is taken.

Options

A. 60
B. 120
C. 110
D. 75

Answer

To find the number of combinations that can be formed with 5 oranges, 4 mangoes, and 3 bananas when one fruit of each kind is taken, we can follow these steps:

### Step 1: Identify the number of choices for each type of fruit
- For oranges, we have 5 options (5 oranges).
- For mangoes, we have 4 options (4 mangoes).
- For bananas, we have 3 options (3 bananas).

### Step 2: Calculate the number of combinations for each type of fruit
- The number of ways to choose 1 orange from 5 is given by the combination formula \( \binom{5}{1} \).
- The number of ways to choose 1 mango from 4 is given by \( \binom{4}{1} \).
- The number of ways to choose 1 banana from 3 is given by \( \binom{3}{1} \).

### Step 3: Apply the combination formula
The combination formula is:
\[ \binom{n}{r} = \frac{n!}{r!(n-r)!} \]
For our case:
- \( \binom{5}{1} = \frac{5!}{1!(5-1)!} = \frac{5!}{1! \cdot 4!} = 5 \)
- \( \binom{4}{1} = \frac{4!}{1!(4-1)!} = \frac{4!}{1! \cdot 3!} = 4 \)
- \( \binom{3}{1} = \frac{3!}{1!(3-1)!} = \frac{3!}{1! \cdot 2!} = 3 \)

### Step 4: Multiply the number of combinations
Now, we multiply the number of ways to choose each fruit:
\[ \text{Total combinations} = \binom{5}{1} \times \binom{4}{1} \times \binom{3}{1} = 5 \times 4 \times 3 \]

### Step 5: Calculate the total
Calculating the total:
\[ 5 \times 4 = 20 \]
\[ 20 \times 3 = 60 \]

### Conclusion
Thus, the total number of combinations that can be formed is **60**.

---