A traveler has 7 pieces of luggage. How many ways can he select 3 pieces of luggage for a trip?
a. 5040
b. 210
c. 35
d. 28
Nvm that's not right
35
To find the number of ways the traveler can select 3 pieces of luggage out of the 7 available, we can use the concept of combinations. In this case, the order of the selected luggage does not matter.
The formula for combinations is given by:
C(n, r) = n! / (r! * (n - r)!)
Where n represents the total number of items, and r represents the number of items to be chosen.
In this particular scenario, we need to calculate C(7, 3):
C(7, 3) = 7! / (3! * (7 - 3)!)
Simplifying this expression:
C(7, 3) = 7! / (3! * 4!)
Using the definition of a factorial:
C(7, 3) = (7 * 6 * 5 * 4!) / (3! * 4!)
The factorials in the numerator and denominator will cancel out:
C(7, 3) = (7 * 6 * 5) / (3 * 2 * 1)
C(7, 3) = 35
Therefore, the traveler can select 3 pieces of luggage for the trip in 35 different ways.
The correct answer is c. 35.