Question

A classroom has only eight vacant seats, three in the front row and five in the back row. In how many ways can five additional students be seated if two of them insist on sitting on the front row?

Answer 1

just go through seating them in order...
1st has 3 choices in front row, once he's seated the 2nd student has 2 seat choices left.
now there 5-2 = 3 students left to seat. there are 8-2 = 6 seats remaining as there are no more restrictions on where they can sit.
so 3rd student has 6 choices, the 4th student has 5, and the last has 4 choices.
so multiplying them: 3 x 2 x 6 x 5 x 4 = ?

try not to depend on formulas too much for these kinds of probs -- logic and counting work best as you work through it