A teacher has 30 students in a classroom. She has 6 seats in the front row. How many ways can she arrange her students to sit in the front row ?
A. 431, 000
B. 593, 775
C. 427, 518, 000
D. 729, 000, 000

C. 427, 518, 000

Step-by-step explanation:

-This is a permutation problem.

-A recognition of of permutation of six  from a group of 30.

-Hence, the different number of ways is calculated as:

The students can be arranged in 427, 518, 000  ways

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!