26. Seven students are to have a
jolly good time together. If they
are to be seated, find the number
of ways they are to be chosen.
A. 5040
B. 6040
C. 4050
C. 4050
D. 4060
The number of ways to choose and seat the seven students can be found using the formula for permutations, which is n! / (n-r)!, where n is the total number of objects and r is the number of objects being chosen.
In this case, n = 7 (the number of students) and r = 7 (all of the students are being chosen).
So the number of ways they can be chosen and seated is 7! / (7-7)! = 7! / 0! = 7! / 1 = 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040.
Therefore, the answer is A. 5040.
To find the number of ways the seven students can be chosen, we need to calculate the number of permutations.
The formula for permutations is given by nPr = n! / (n-r)!, where n is the total number of objects and r is the number of objects being chosen.
In this case, n = 7 (since there are seven students) and r = 7 (since we want to choose all seven students).
So, the number of ways the seven students can be chosen is given by 7P7 = 7! / (7-7)! = 7! / 0! = 7!/1 = 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040 ways.
Therefore, the correct answer is A. 5040.