Question

Suppose a travel agent is proposing packages for clients to

visit five out of a list of eleven particular European cities. How
many travel routes could be selected?

Answer 1

The number of travel routes that can be selected from a list of 11 cities is 462.

Step-by-step explanation:

The number of travel routes that can be selected can be determined using the combination formula. In this case, we want to select 5 cities out of a list of 11. The combination formula is given by:

C(n, r) = n! / (r! * (n - r)!)

Where n is the total number of options and r is the number of options to be selected. Plugging in the numbers:

C(11, 5) = 11! / (5! * (11 - 5)!)

Simplifying the formula:

C(11, 5) = 11! / (5! * 6!)

C(11, 5) = (11 * 10 * 9 * 8 * 7) / (5 * 4 * 3 * 2 * 1)

C(11, 5) = 462

Therefore, there are 462 travel routes that can be selected.