Josie wants to make a sandwich with 4 kinds of vegetables on it, but there are 10 vegetables to choose from in her refrigerator. In how many sequences can she layer 4 of them on her sandwich?
Question
Josie wants to make a sandwich with 4 kinds of vegetables on it, but there are 10 vegetables to choose from in her refrigerator. In how many sequences can she layer 4 of them on her sandwich?
Solution
To solve this problem, we need to use the concept of permutations because the order in which Josie layers the vegetables on her sandwich matters.
The formula for permutations is:
P(n, r) = n! / (n-r)!
where:
- n is the total number of options,
- r is the number of options chosen at a time,
- "!" denotes a factorial, which means multiplying all positive integers up to that number.
In this case, n = 10 (the total number of vegetables) and r = 4 (the number of vegetables Josie wants on her sandwich).
So, the calculation would be:
P(10, 4) = 10! / (10-4)!
= 10987654321 / 654321
= 1098*7
= 5040
So, Josie can layer the 4 vegetables on her sandwich in 5040 different sequences.
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