8 people are boarding an aircraft. 2 have tickets for first class and board before those in the economy class. In how many ways can the eight people board the aircraft?

Explain how you get your answer, please.

Question

8 people are boarding an aircraft. 2 have tickets for first class and board before those in the economy class. In how many ways can the eight people board the aircraft?

Explain how you get your answer, please.

anonymous · Answer

2 choices for the first seat
1 for the second seat in first class
then 6 for the third seat
5 for the fourth
4 for the fifth
3 for the sixth
2 for the seventh
1 for the eighth
by the counting principle you multiply these together to get your answer

anonymous · Answer

more succinctly written as 
$$2\times 6!$$

anonymous · Answer

so, what about a faster way, like using 2! + 6! or something like that

anonymous · Answer

why wouldn't it be 2! x 6!
or is it and you just take out the ! on 2 because 2! =2?