SOLUTION: There are 7 students in a class. If there are 3 seats in the front row, how many ways can the students sit in the front row, assuming there are no empty seats?

Algebra ->  Permutations -> SOLUTION: There are 7 students in a class. If there are 3 seats in the front row, how many ways can the students sit in the front row, assuming there are no empty seats?      Log On


   

Question 1143996: There are 7 students in a class. If there are 3 seats in the front row, how many ways can the students sit in the front row, assuming there are no empty seats?
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
P( 7,3 ) = +7%21+%2F+%28+7+-+3+%29%21+
P( 7,3 ) = +%28+7%2A6%2A5%2A4%2A3%2A2%2A1+%29+%2F+%28+4%2A3%2A2%2A1+%29+
P( 7,3 ) = +7%2A6%2A5+
P( 7,3 ) = +210+ ways
Use permutations because the order of the seating matters

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

Any of the 7 students may seat at the chair #1        (7 options).


Any of remaining 6 students can seat at the chair #2  (6 options)


Any of remaining 5 students can seat at the chair #3  (5 options)



Thus, in all,  7*6*5 = 210 different ways (placements) are possible.     ANSWER