→in an election race for president, treasurer, and secretary
→arranging letters in a word
→calling out a ticket number for a door prize
However, in some situations order doesn’t matter. We call this a combination.
For example: – in a hand of poker a “full house” is a “full house” (eg. 3 aces and 2 jacks) regard less of the order the cards were dealt.
– in Lotto Max or Lotto 6149,if your numbers match you are a winner, regardless of when the numbers were selected.
Combinations can be calculated in a similar manner as permutations. To avoid duplications, (naturally in occur in combinations) one must divide by the “extra” factorial present. This concept of “extra” factorial will be explored in the first example.
2.3 – THE PRINCIPLE OF INCLUSION AND EXCLUSION
Mr. Wilson coaches the basketball team and the volleyball team. There are 15 members on the basketball team and 13 members on the volleyball team. Both teams are playing in a tournament at the same school and the coach orders a bus that fits 24 people.
The principle of inclusion and exclusion gives a formula for finding the number of items in the union of two or
n(A or B) = n(A)+n(B)-n(A and B) or n(A ∪ B)= n(A)+n(B)-n(A ∩ B)
n(A ∪ B ∪ c) = n(A) + n(B) + n(c) – n(A ∩ B)- n(A ∩ c)-n(B ∩ c) + n(A ∩ B ∩ c)
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