What is the probability of two points appearing three times when you roll the dice eight times? Find a detailed explanation.

When a dice is thrown eight times, there are 6 8 =1679616 possibilities, three times when two points appear, and three times when c (8 8,3) * 5 5 =175000 possibilities (three times out of eight when two points appear, and five possibilities each time).

Dice (tóu zi), also known as Sh m 4 i zi, is a throwing tool used in traditional folk entertainment in China. As early as the Warring States period, it was usually used as a prop for table games. The most common dice is a six-sided dice, which is a regular cube with one to six holes (or numbers) on it, and the sum of the numbers on its two opposite sides must be seven.

Dice is one of the indispensable tools for many recreational activities, such as playing mahjong and Pai Jiu. Dice here refers to gambling that depends solely on dice to decide whether to win or lose. Usually used to gamble on size. In sic bo, idle people bet on bookmakers. Before each bet, the dealer puts three dice in a covered vessel and shakes them. When the idlers have finished betting, the dealer opens the utensils and gives out prizes.

Historical source

According to legend, the inventor of dice is Cao Zhi, a writer in the Three Kingdoms period. Originally used as a tool for divination, it later evolved into a game of concubines in the harem, betting on wine or silk sachets with dice points. At that time, the dots on the dice were all painted black, and it was not until the Tang Dynasty that red strokes were added.

However, according to textual research, the dice unearthed from Qi Tomb in Qingzhou, Shandong Province were not invented by Cao Zhi. Dice, as one of the six major operas in China, is regarded as the ancestor of China's operas, and it was popular as early as the late Spring and Autumn Period and the Warring States Period.