To solve this problem, we can use the concept of permutations. A permutation is an arrangement of objects in a specific order. The order of arrangement of the object is very important. The number of permutations of n objects taken r at a time is given by:

P(n, r) = n! / (n-r)!

where n! denotes the factorial of n.

In this case, Hayley has 7 different fish and she wants to transfer 3 of them to a new tank. The order in which she transfers the fish matters (for example, transferring fish A, then B, then C is a different sequence than transferring fish B, A, C). So we are looking for the number of permutations of 7 objects taken 3 at a time.

P(7, 3) = 7! / (7-3)!

= 7*6*5*4*3*2 / 4*3*2

= 7*6*5

= 210

So, there are 210 different sequences in which Hayley can transfer the fish to the new tank.

Question

To solve this problem, we can use the concept of permutations. A permutation is an arrangement of objects in a specific order. The order of arrangement of the object is very important. The number of permutations of n objects taken r at a time is given by:

P(n, r) = n! / (n-r)!

where n! denotes the factorial of n.

In this case, Hayley has 7 different fish and she wants to transfer 3 of them to a new tank. The order in which she transfers the fish matters (for example, transferring fish A, then B, then C is a different sequence than transferring fish B, A, C). So we are looking for the number of permutations of 7 objects taken 3 at a time.

P(7, 3) = 7! / (7-3)!

= 7*6*5*4*3*2 / 4*3*2

= 7*6*5

= 210

So, there are 210 different sequences in which Hayley can transfer the fish to the new tank.

Knowee AI · Accepted Answer

To solve this problem, we can use the concept of permutations. A permutation is an arrangement of objects in a specific order. The order of arrangement of the object is very important. The number of permutations of n objects taken r at a time is given by:

P(n, r) = n! / (n-r)!

where n! denotes the factorial of n.

In this case, Hayley has 7 different fish and she wants to transfer 3 of them to a new tank. The order in which she transfers the fish matters (for example, transferring fish A, then B, then C is a different sequence than transferring fish B, A, C). So we are looking for the number of permutations of 7 objects taken 3 at a time.

P(7, 3) = 7! / (7-3)!

= 7*6*5*4*3*2 / 4*3*2

= 7*6*5

= 210

So, there are 210 different sequences in which Hayley can transfer the fish to the new tank.

Hayley has 7 different fish in a small, crowded tank. She decides to randomly scoop up individual fish and transfer them to a new tank until a total of 3 fish have been moved. How many sequences of 3 fish are possible?

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