Warren has 5 different fish in a small, crowded tank. He decides to randomly scoop up individual fish and transfer them to a new tank until a total of 4 fish have been moved. How many sequences of 4 fish are possible?
sequences?
The number of sequences of 4 fish that can be moved from the tank can be calculated using combinations. We need to choose 4 fish out of 5, without regard to order. This can be represented mathematically as:
5 choose 4 = 5C4 = 5!/((5-4)!4!) = 5
Therefore, there are only 5 possible sequences of 4 fish that can be moved from the tank.
To determine the number of sequences of 4 fish that can be moved from the tank, we can use the combination formula.
The formula to calculate the number of combinations is:
C(n, r) = n! / (r! * (n-r)!)
Where:
n = total number of fish in the tank (5)
r = number of fish to be moved (4)
Using the formula, we have:
C(5, 4) = 5! / (4! * (5-4)!)
C(5, 4) = 5! / (4! * 1!)
C(5, 4) = (5 * 4 * 3 * 2 * 1) / ((4 * 3 * 2 * 1) * 1)
C(5, 4) = 5
Therefore, there are 5 different sequences of 4 fish that can be moved from the tank.