Quincy wants to make a sandwich with 3 kinds of vegetables on it, but there are 9 vegetables to choose from in his refrigerator. In how many sequences can he layer 3 of them on his sandwich?
Question
Quincy wants to make a sandwich with 3 kinds of vegetables on it, but there are 9 vegetables to choose from in his refrigerator. In how many sequences can he layer 3 of them on his sandwich?
Solution
To solve this problem, we can use the concept of permutations in combinatorics. A permutation is an arrangement of objects in a specific order. The number of permutations of n objects taken r at a time is given by the formula:
P(n, r) = n! / (n-r)!
where "!" denotes factorial, which is the product of all positive integers up to that number.
In this case, Quincy has 9 vegetables to choose from (n=9) and he wants to choose 3 of them (r=3). So we can plug these values into the formula:
P(9, 3) = 9! / (9-3)!
= 987654321 / 65432*1
= 987
= 504
So, Quincy can layer the 3 vegetables on his sandwich in 504 different sequences.
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