Total Number of Combinations


 
 
Concept Explanation
 

Total Number of Combinations

Let us consider some cases to calculate the total number of combinations

1.The total number of combination of ( p + q) things taken any number at a time when p things are alike of one kind and q things are alike of a second kind is

( p + 1)(q + 1) -1.

For Example:, There are 4 orange, 5 pineapples and 7 watermelons in a fruits basket. The number of ways in which a person can choose one or more of the fruits is [(4 + 1) X ( 5 + 1) X ( 7 + 1)] -1

                                           = ( 5 X 6 X 8 ) - 1 = 239

2. The total number of ways of selecting one or more objects from n given objects is

(2^n - 1).

 For Example:The number of ways in which a man can invite one or more of his 5 friends to dinner is (2^5-1) = 32- 1 = 31.

3. Total number of selection of r consecutive things out of n things in a row

= n - r + 1.

For Example: Total ways of selecting 3 consecutive students from a row of 9 students

                                    =  9 - 3 + 1 = 7 ways

4. Number of selections of r consecutive things out of n things along a circle

= {n, when r > n

   { 1, when r = n

For Example:, Total ways in which 9 pearls can be selected from a necklace having 24 pearls is 24.

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