Question

ThreeThree friends board an airliner just before departure time. There are only 1010 seats​ left, 44 of which are aisle seats. How many ways can the 33 people arrange themselves in available seats so that at least one of them sits on the​ aisle? The 3 people can arrange themselves in how many ways.

Answer 1

Na = 720 - 120 = 600 ways

The 3 people can arrange themselves in 600 possible ways.

Explanation:

For at least one of the three friends to seat on an aisle seat, the number of possible arrangements can be given as;

Na = Nt - Nn .....1

Where;

Na = number of possible arrangements with at least one of the seating on an aisle seat.

Nt = total number of possible arrangements for the three friends

Nn = number of possible arrangements with none of the three friends seating on an aisle seat.

Given;

Total number of seats available = 10

Total number of aisle seats available = 4

Total number of people = 3

So;

Nt = 10C3 = 10×9×8 = 720

Nn = (10-4)C3 = 6C3 = 6×5×4 = 120

From equation 1;

Na = 720 - 120 = 600 ways

The 3 people can arrange themselves in 600 possible ways.