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.

B.210