90+ Permutations Combination And Probability Question PDF

• • Permutation: It is the different arrangements of a given number of elements taken one by one, or some, or all at a time. For example, if we have two elements A and B, then there are two possible arrangements, AB and BA.
  • Number of permutations when ‘r’ elements are arranged out of a total of ‘n’ elements is ⁿP_r = n! / (n – r)!. For example, let n = 4 (A, B, C and D) and r = 2 (All permutations of size 2). The answer is 4!/(4-2)! = 12. The twelve permutations are AB, AC, AD, BA, BC, BD, CA, CB, CD, DA, DB and DC.
  • Combination: It is the different selections of a given number of elements taken one by one, or some, or all at a time. For example, if we have two elements A and B, then there is only one way select two items, we select both of them.
  • Number of combinations when ‘r’ elements are selected out of a total of ‘n’ elements is ⁿ C _r = n! / [ (r !) x (n – r)! ]. For example, let n = 4 (A, B, C and D) and r = 2 (All combinations of size 2). The answer is 4!/((4-2)!*2!) = 6. The six combinations are AB, AC, AD, BC, BD, CD.
  • ⁿ C _r = ⁿ C _{(n – r)}

NOTE: In the same example, we have different cases for permutation and combination. For permutation, AB and BA are two different things but for selection, AB and BA are the same.