Probability-Combinatorics
Combinatorics The different combinations from specific finite sets It has some restrictions 1. Repetition 2. Order 3. Different Criteria So we have 3 things 1. Permutation 2. Variations 3. Combinations # No of favorable outcomes # No of all elements in a sample space Permutations The number of different possible ways we can arrange a set of elements P n = n x (n-1) x (n-2)x............ 1 = n! n! = Product of numbers from 1 to n Negative numbers don't have factorial 0!=1 Example 6! = 5! x 6 7! = 6! x 7 (n + k)! and (n - k )! (n + k)!= n! x ( n+1) x (n+2) x .......(n+k) (n - k)!= n! (n - k + 1) x ( n - k + 2)..........x n n > k n!/k!= ( k + 1) x ( k + 2) x ............... x n 7!/4!= 5 x 6 x 7 Variations The total number of ways w...