Can You Use Toothpicks As Earrings

Challenge - Techniques

A candidate for president wants to visit 8 cities. How many ways can order the first three visits?

A) 3! , B) 8, C) 56, D) 336, E) 8!

Answer:

First line of reasoning: the first visit I can choose 8 cities in the second only between 7 (and I visited it before) and at the third visit by 6. by the multiplicative principle I can organize the visit of 8 x 7 x 6 = 336 ways.

second way of thinking: This is clearly an exercise in permutations. Must permute 8 cities in 3, ie

P (8,3) = 8! / (8-3)! = 8! / 5! = (8 x 7 x 6 x 5!) / 5! = 8 x 7 x 6 = 336 ways.

Alternative D)

Source: Santillana - 3rd. Medium.

NEM: Tercero Medio.

Main Topic: III) Probability and Statistics.

CMO: Counting Techniques.