Answer :
Final answer:
There are 924 combinations for a fruit salad consisting of 6 different fruits selected from 12 different kinds. This is calculated using the combinations formula C(n, r). By substituting n = 12 and r = 6 into the formula, we arrive at the total number of combinations.
Explanation:
Combinations of Fruits in a Salad
To determine how many combinations are possible for a fruit salad consisting of 6 different fruits selected from 12 different kinds, we will use the concept of combinations.
The formula for calculating combinations is given by:
C(n, r) = n! / (r! (n - r)!)
Where:
- n is the total number of items (in this case, the different kinds of fruits),
- r is the number of items to choose (in this case, the 6 fruits for the salad),
- ! denotes factorial, which is the product of all positive integers up to that number.
Using the values:
- n = 12
- r = 6
Now, we can substitute these values into the combination formula:
C(12, 6) = 12! / (6! (12 - 6)!) = 12! / (6! * 6!)
Calculating this further:
C(12, 6) = (12 × 11 × 10 × 9 × 8 × 7) / (6 × 5 × 4 × 3 × 2 × 1) = 924
Therefore, there are 924 combinations possible for a fruit salad consisting of 6 different fruits selected from 12 different kinds.
Learn more about combinations here:
https://brainly.com/question/30646507
