What is Combination ?
Each of the different groups or selections which can be formed by taking some or all of a number of objects, is called a combination. In combination we can select only one item at time it based on selection on choice.
Suppose Ball , Marbel, etc.
Type 1: Suppose we want to select two out of three girls A, B, C. Then possible selection are AB, BC, and CA.
Note: that AB and BA represent the same selection.
Type 2: Suppose We select all three girls Like A, B, C. Then the selection is ABC.
Note: BAC, ABC, CAB are the same choice of selection.
Type 3: All the combinations formed by a, b, c, taking two at a time are ab, bc, ca.
Type4: The only combinations that can be formed of three letters a, b, c taken all at a time is abc.
Type5: Various person of 2 out of four person A, B, C, D are : AB, AC, AD, BC, BD, CD.
Type6: Note that ab and ba are two different permutations but they represent the same combination.
Number of Combinations : The number of all combinations of n things, taken r at a time is :
n C r = n! / r! ( n – r ) ! = n ( n – 1 ) ( n – 2 ) …….to r factors / r!.
Note: if n = r , nCr = 1 and n C 0 = 1.
Important Rule:
nCr = n C (n – r ). = 1.
Ex: 16 C 13 = 16 C ( 16 – 13 ) = 16 C 3 = 16 x 15 x 14 x 13! / 3! = 16 x 15 x 14 / 3 x 2 x 1 = 560
Find out value of 10 P 3
= 10 C 3= 10 x 9 x 8 / 3! = 10 x 9 x 8 / 3 x 2 x 1 = 120
Find the value of 50 C 50
= 50 C 50 = 1. [ n C n = 1]
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