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Answer :
To determine the number of different ways to prepare a vegetable salad and a fruit salad, we can use the concept of combinations.
With 5 types of vegetables and 4 types of fruit, we calculate the number of combinations for each type of salad. Additionally, to find the number of ways to prepare two different kinds of salad, we can multiply the number of options for each type of salad.
To prepare a vegetable salad, we need to choose any 2 types of vegetables out of the 5 available. The number of combinations for this is given by the formula C(5, 2), which represents choosing 2 items from a set of 5. Evaluating this expression, we find that there are 10 different ways to prepare a vegetable salad.
Similarly, to prepare a fruit salad, we need to choose any 2 types of fruit out of the 4 available. The number of combinations for this is given by C(4, 2), which evaluates to 6 different ways to prepare a fruit salad.
To prepare two different kinds of salad, we need to consider the options for each type of salad separately. For each vegetable salad, there are 10 possible combinations. For each fruit salad, there are 6 possible combinations. Therefore, to find the total number of ways to prepare two different kinds of salad, we multiply the number of options for each type: 10 * 6 = 60 different ways.
In conclusion, there are 10 different ways to prepare a vegetable salad, 6 different ways to prepare a fruit salad, and a total of 60 different ways to prepare two different kinds of salad, considering the given number of vegetable and fruit types.
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