LEARNER'S KENTRO

  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...

  Probability The likelihood of an event occurring  What is an Event For Understanding, We take the example of flipping a coin There will be 2 Chance  Head  <-----------------> Tails Chance occurring is an event So, the event will be likely or unlikely to happen For Event Occurring --> 1 For Event not Occurring ---> 0 Define Formula A --> Event' P(A) --> Probability For Coin                  P(A) = 1/2= 0.5 For Dice               P(A) = 1/6 =~ 0.167 So, Now We have to see the Probability of Two independent events same time             P( A and B ) = P(A). P(B) Expected Values The average Outcome we expect if we run an experiment many times There are two kinds of Probability 1. Experimental Probability - 80 %  2. Theoretical ( True) Probability- 20% Experimental Probability – The probability we assign an event, based on an expe...