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Answer :
Final answer:
The editor can choose to review 5 fiction manuscripts and 3 non-fiction manuscripts in 4410 different ways.
Explanation:
To find the number of ways the editor can choose to review 5 fiction manuscripts and 3 non-fiction manuscripts, we can use the concept of combinations.
There are 9 fiction manuscripts, and we need to choose 5 of them. This can be represented as C(9, 5), which is the number of ways to choose 5 items from a set of 9 items without regard to order.
Similarly, there are 7 non-fiction manuscripts, and we need to choose 3 of them. This can be represented as C(7, 3).
The total number of ways to choose the manuscripts is the product of these two combinations: C(9, 5) * C(7, 3).
Using the formula for combinations, C(n, r) = n! / (r! * (n-r)!) where n is the total number of items and r is the number of items to be chosen, we can calculate the answer as follows:
C(9, 5) * C(7, 3) = (9! / (5! * (9-5)!)) * (7! / (3! * (7-3)!)) = (9 * 8 * 7 * 6 * 5) / (5 * 4 * 3 * 2 * 1) * (7 * 6 * 5) / (3 * 2 * 1) = 126 * 35 = 4410.
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Final answer:
The editor can choose 5 fiction and 3 non-fiction manuscripts in (9 choose 5) * (7 choose 3) ways.
Explanation:
The editor has 9 fiction manuscripts and can choose 5 of them, which can be done in 9 choose 5 ways. Similarly, the editor has 7 non-fiction manuscripts and can choose 3 of them in 7 choose 3 ways. Since these selections are independent, the editor can choose 5 of the fiction manuscripts and 3 of the non-fiction manuscripts in (9 choose 5) * (7 choose 3) ways.
Learn more about Combinations and Permutations here:
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