b:head_first_statistics:permutation_and_combination
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| b:head_first_statistics:permutation_and_combination [2019/10/28 11:44] – [e.g.] hkimscil | b:head_first_statistics:permutation_and_combination [2023/10/11 08:16] (current) – [e.g.] hkimscil | ||
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| + | ====== Permutation and Combination ====== | ||
| + | 순열과 조합 | ||
| ====== Permutation ====== | ====== Permutation ====== | ||
| + | |||
| 세마리 말이 들어오는 순서 | 세마리 말이 들어오는 순서 | ||
| {{: | {{: | ||
| Line 69: | Line 72: | ||
| b, a2, a1 | b, a2, a1 | ||
| - | n! / p! x q! | + | $$ \frac {n!} {p! * q!} $$ |
| + | < | ||
| {{: | {{: | ||
| + | |||
| 6 horses | 6 horses | ||
| 2 groups 3 horses per each group | 2 groups 3 horses per each group | ||
| + | |||
| + | {{: | ||
| < | < | ||
| Line 88: | Line 94: | ||
| {{: | {{: | ||
| {{: | {{: | ||
| + | |||
| + | <WRAP box> | ||
| + | X = {a a b c c c} 라면? | ||
| + | n(X) = 6 이므로 총 6! | ||
| + | a가 둘, c가 셋으로 묶이므로 | ||
| + | 6! / (2! * 3!) | ||
| + | = 6*5*2 = 60 | ||
| + | |||
| + | |||
| + | </ | ||
| <WRAP box> | <WRAP box> | ||
| Line 150: | Line 166: | ||
| C A | C A | ||
| + | \begin{eqnarray*} | ||
| + | _{3}P_{2} & = & \frac{3!}{(3-2)!} \\ | ||
| + | & = & \frac {3!}{(3-2)!} = 6 | ||
| + | \end{eqnarray*} | ||
| + | |||
| + | Among the two, the order doesn' | ||
| 2 representatives | 2 representatives | ||
| A B | B A | A B | B A | ||
| Line 156: | Line 178: | ||
| \begin{eqnarray*} | \begin{eqnarray*} | ||
| - | _{3}C_{2} * 2! & = & _{3}P_{2} \\ | + | \text{Answer we want} & = & \frac {_{3}P_{2}}{2!} \\ |
| - | _{3}C_{2} & = & \frac {_{3}P_{2}}{2!} \\ | + | \text{We call this} & = & _{3}C_{2} \\ |
| _{3}C_{2} & = & \frac {\frac{3!}{(3-2)!}} {\frac {2!} {1}} \\ | _{3}C_{2} & = & \frac {\frac{3!}{(3-2)!}} {\frac {2!} {1}} \\ | ||
| - | _{3}C_{2} & = & \frac {3!}{2! * (3-2)!} = 6 | + | _{3}C_{2} & = & \frac {3!}{2! * (3-2)!} = 3 |
| \end{eqnarray*} | \end{eqnarray*} | ||
| Line 195: | Line 217: | ||
| 2. The coach classes 3 of the players as expert shooters. What’s the probability that all 3 of these players will be on the court at the same time, if they’re chosen at random? | 2. The coach classes 3 of the players as expert shooters. What’s the probability that all 3 of these players will be on the court at the same time, if they’re chosen at random? | ||
| </ | </ | ||
| + | |||
| < | < | ||
| ## n! / r!(n-r)! | ## n! / r!(n-r)! | ||
| Line 233: | Line 256: | ||
| A flush is where all 5 cards belong to the same suit. What’s the probability of getting this? | A flush is where all 5 cards belong to the same suit. What’s the probability of getting this? | ||
| </ | </ | ||
| + | {{https:// | ||
| + | see [[wp> | ||
| + | {{https:// | ||
| < | < | ||
| ## 52장의 카드 중에서 5장 고를 조합은 | ## 52장의 카드 중에서 5장 고를 조합은 | ||
b/head_first_statistics/permutation_and_combination.1572230695.txt.gz · Last modified: 2019/10/28 11:44 by hkimscil