02.28.2017. Tuesday
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 Thinking Operations
Binomial theorem
⦿ Binomial theorem
Combinatorics
⦿ Permutations
⦿ Combination
⦿ Variation
Sets
⦿ Operations on Sets
Logic
⦿ Logical Operations and Truth Tables


Combinatorics

Combination

Combination without Repetition

A combination is a way of selecting k items from a collection of n items (k ≤ n), such that (unlike permutations) the order of selection does not matter. The repetition of items is not allowed.

The number of combinations::

C n k = n · ( n 1 ) · ( n 2 ) · . . . ( n k + 1 ) k ! = n ! k ! · ( n k ) ! = ( n k )

Example:

From 5 items {a,b,c,d,e} choose 2,  repetition is not allowed: C 5 2 = 5 ! 2 ! · ( 3 ) ! = ( 5 3 ) = 10

(a,b), (a,c), (a,d), (a,e), (b,c), (b,d), (b,e), (c,d), (c,e), (d,e)

Combination without Repetition

A combination is a way of selecting k items from a collection of n items, such that (unlike permutations) the order of selection does not matter. The repetition of items is allowed.

The number of combinations:

C ¯ n k = ( n + k 1 k )

Example:

From 4 items {a,b,c,d} choose 2 items, repetition is allowed:

The number of combinations: C ¯ 4 2 = ( 4 + 2 1 2 ) = ( 5 2 ) = 10

(a,a), (a,b), (a,c), (a,d), (b,b), (b,c), (b,d), (c,c), (c,d), (d,d)