There are 3 passengers hoping to get a seat on the next flight to Chicago, but there are only 2 seats left on the plane. In how many ways can the seats be filled?
Question
There are 3 passengers hoping to get a seat on the next flight to Chicago, but there are only 2 seats left on the plane. In how many ways can the seats be filled?
Solution
This is a problem of combinations. We are choosing 2 passengers (seats) from a group of 3 passengers. The formula for combinations is:
C(n, k) = n! / [k!(n-k)!]
where:
- n is the total number of options,
- k is the number of options to choose,
- "!" denotes a factorial, meaning to multiply a series of descending natural numbers.
Here, n = 3 (the total number of passengers) and k = 2 (the number of available seats).
So, the calculation is:
C(3, 2) = 3! / [2!(3-2)!] = (321) / [(21)(1)] = 6 / 2 = 3
So, there are 3 different ways the 2 seats can be filled by the 3 passengers.
Similar Questions
A group of 6 friends goes to the movies, but when they get into the theater there are only 3 seats left in the front row. In how many ways can the friends fill the seats in the front row?
There are 7 candidates for 3 seats, in how many ways the post be filled?
Three persons enter in a railwaycompartment. If there are 5 seats vacant,in how many ways they can take theses
There are 3 seats in a row. In how many different ways can 5 boys occupy them?
A joint family in a town has a grandmother, five children and two grandchildren. In how many ways can the seating arrangement be made such that the grandchildren occupy both the seats at the end and the grandmother sits with her children on either side of her?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.