1-24 ■ Counting These exercises involve counting.

Airline Flight Bookings An airline company has overbooked a particular flight, and seven passengers must be “bumped” from the flight. If 120 passengers are booked on this flight, in how many ways can the airline choose the seven passengers to be bumped?

To find:

The total number of ways to choose the seven passengers to be bumped.

Given:

The total booking is of 120 passengers.

The number of passengers bumped from the flight are 7.

Approach:

If a set has n objects, then the number of ways of ordering the r elements subset of the set is denoted P(n,r) and is called the number of permutation of n objects taken r at a time and given by,

P(n,r)=n!(n−r)!

Calculation:

Calculate the total number of ways to choose the seven passengers to be bumped.

Substitute 120 for n, and 7 for r in the above formula.