Question

At the beginning of class , Charise teachermakes an offer to the students. She will dismiss the class early if they can make all possible arrangements with the 13 students in the class in a single-file line. How many such arrangements of the 13 students are possible?

A) 13
B) 78
C) 169
D) 6227020800.

Answer 1

The number of arrangements of the 13 students in a single-file line is calculated using permutations, resulting in 6227020800 possible arrangements.

Step-by-step explanation:

To determine how many different arrangements of the 13 students are possible in a single-file line, we need to calculate the number of permutations of 13 distinct objects. This is a straightforward application of the formula for permutations:

P(n) = n!, where n is the number of objects to arrange and n! denotes the factorial of n.

For 13 students, the calculation is:

13! = 13 × 12 × 11 × 10 × ... × 3 × 2 × 1

= 6227020800 possible arrangements.

Thus, the correct answer is D) 6227020800.