A tourist in Ireland wants to visit 6 different cities. How many different routes are possible

720

To find the number of different routes the tourist can take to visit 6 different cities in Ireland, we can use the concept of permutations.

A permutation is an arrangement of objects in a specific order. In this case, we want to find the number of different ways the tourist can visit the 6 cities, assuming that each city is visited only once.

Since the order of the cities matters, we can use the formula for permutation:

P(n, r) = n! / (n - r)!

Where n is the total number of cities (6 in this case), and r is the number of cities visited in each route (also 6 since all cities need to be visited).

So, the number of different routes is:

P(6, 6) = 6! / (6 - 6)!
= 6! / 0!
= 6! / 1
= 6 * 5 * 4 * 3 * 2 * 1 / 1
= 720

Therefore, there are 720 different routes that the tourist can take to visit all 6 cities in Ireland.