A hockey team is lining up in a row for a group photo there team has one goalie four defence and seven forwards the photographer wants the defence on one side of the goalie and the forwards on the other side how many ways can the team stand in a row for this pose

4 d

7 f
2 sides

4! * 7! * 2

i think its 21

To determine the number of ways the team can stand in a row for this pose, we need to consider the following factors:

1. Goalie's position: The goalie can only stand in one specific position since there is only one goalie.

2. Defense's position: There are four defense players who need to stand together on one side of the goalie. The four defense players can be rearranged among themselves, resulting in 4! (4 factorial) arrangements.

3. Forwards' position: There are seven forward players who need to stand on the other side of the goalie. The seven forward players can be rearranged among themselves, resulting in 7! (7 factorial) arrangements.

Therefore, the total number of ways the team can stand in a row for this pose can be calculated by multiplying the number of arrangements for the defense players and forward players together:

4! * 7!

Now, let's calculate the value:

4! (4 factorial) = 4 * 3 * 2 * 1 = 24
7! (7 factorial) = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040

Therefore, the total number of ways the team can stand in a row for this pose is:

24 * 5,040 = 120,960 ways.

To determine the number of ways the team can stand in a row for this pose, we can break down the problem into steps:

Step 1: Determine the number of ways to arrange the goalies and the defense.
Since there is only one goalie and four defense players, we calculate the number of ways to arrange them as 5!.

Step 2: Determine the number of ways to arrange the forwards.
Since there are seven forwards, we calculate the number of ways to arrange them as 7!.

Step 3: Multiply the results from Step 1 and Step 2.
To obtain the total number of ways to arrange the team, we multiply the results from Step 1 and Step 2: 5! * 7!.

Step 4: Account for the positioning of the two groups.
In this specific case, we need to consider that the defense should be on one side of the goalie, and the forwards on the other side. This means we can arrange both groups in any order, which we can calculate using the concept of permutations. The number of permutations for two groups can be determined by 2!.

Step 5: Multiply the result from Step 3 by the result from Step 4.
We multiply the total number of ways to arrange the team (from Step 3) by the number of permutations for the two groups (from Step 4): (5! * 7!) * 2!

Step 6: Calculate the final answer.
By applying the above steps, we can determine the number of ways the team can stand in a row for this pose. Evaluating the expression from Step 5 yields our final answer.

Therefore, the total number of ways the team can stand in a row for this pose is (5! * 7!) * 2!.