Question

in a function, 2 'A' cars and 5 'B' cars are arranged to receive 31 guests from airport.

Assuming that two particular guests depart by the same car A. In how many ways can they depart ( four persons can sit in car A and five in car B)

Answer 1

31 people total, 2 in car A, leaving 29 others

1st A car then has 29C2 choices
2nd car A has 27C4 choices
The B cars have 25C5, 20C5, 15C5, 10C5, 5C5 choices
now multiply all those results, then multiply by 7! since the cars can leave in any order