out of 6 cheerleaders, 3 will be selected to march in the first row of the parade how many 3-person arrangements can be formed using the 6 cheerleaders if Sandy must stand on the left end of the front row and Dana must also be included in the front row?
A. 2
B. 4
C. 8
D. 10
To solve this problem, we need to determine the number of 3-person arrangements that can be formed using the 6 cheerleaders, with the condition that Sandy must stand on the left end of the front row and Dana must also be included in the front row.
Step 1: Determine the number of ways to place Sandy on the left end.
Since Sandy must stand on the left end, there is only one way to place her.
Step 2: Determine the remaining number of cheerleaders to choose.
Since there are 6 cheerleaders in total and Sandy is already placed, we have 5 cheerleaders remaining to choose from.
Step 3: Determine the number of ways to place Dana.
Since Dana must also be included in the front row, there is only one way to place her.
Step 4: Determine the remaining number of cheerleaders to choose from.
Since Dana is already placed, we have 4 cheerleaders remaining to choose from.
Step 5: Determine the number of ways to place the remaining cheerleaders.
Since there are 4 cheerleaders remaining and we need to choose 1 more to complete the front row, there are 4 ways to place the remaining cheerleaders.
Step 6: Multiply the results from Step 1, Step 3, and Step 5.
The number of 3-person arrangements can be formed using the 6 cheerleaders is 1 x 1 x 4 = 4.
Therefore, the correct answer is B. 4.
Saw this posted before, can't find it, and don't know if it was answered.
Here are the possible arrangements
SDx ---> 4 ways
SxD ---> 4 ways
So what do you think?