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Answer :
Final answer:
The number of different sets of 5+2 bottles that can be chosen is 47880.
Explanation:
To calculate the number of different sets of 5+2 bottles, we need to calculate the number of combinations of 10 red wines taken 5 at a time and 20 white wines taken 2 at a time.
For the red wines, we have 10 different bottles and we need to choose 5. Using the combination formula, we have:
C(10, 5) = 10! / (5!(10-5)!) = 10! / (5! * 5!) = (10 * 9 * 8 * 7 * 6) / (5 * 4 * 3 * 2 * 1) = 252.
For the white wines, we have 20 different bottles and we need to choose 2. Using the combination formula, we have:
C(20, 2) = 20! / (2!(20-2)!) = 20! / (2! * 18!) = (20 * 19) / (2 * 1) = 190.
Now, to calculate the total number of different sets, we multiply the number of combinations for the red wines and the white wines:
Total number of different sets = C(10, 5) * C(20, 2) = 252 * 190 = 47880.
Learn more about counting and combinations here:
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