Recall the FCP and the different formulas of
permutation and combination;
Solve problems involving
permutations and combinations;
and
Appreciate the use of permutation and
combination in solving real-life situations.
Objective
s
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Solving problems involving permutations and combinations requires understanding whether the order of arrangement matters and applying the appropriate formulas to calculate the number of possible arrangements or selections. Mastery of these concepts is essential for tackling a wide range of mathematical, statistical, and real-world problems.
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Recall the FCP and the different formulas of permutation and combination; Solve problems involving permutations and combinations; and Appreciate the use of permutation and combination in solving real-life situations.
Objective
s
Activity 1: Permutation or Combination
Answer:
Choosing 3 questions to answer out of 10
questions in a test.
Combination
Answer:
Drawing a set of 6 numbers containing
numbers 1 to 45.
Combination
Answer:
Selecting 7 letters in an alphabet
Combination
Answer:
Grouping 45 learners with 5 members each
group.
Combination
What do you call the different ways of arranging a set of objects in a specific order or sequential order?
Permutation
What do you call the number ways of selecting from a set when the order is not important?
Combination
How many different
arrangements are
possible for 10 cars in
a line, if 2 are red, 3
are black and 5 are
white?
Given: ๐ =๐
Solution: ๐ท =๐ ๐๐๐ ๐ =๐ ๐ =๐ ๐ท = ๐! ๐! ๐! ๐!
๐ท = ๐๐ ร ๐ ร ๐ ร ๐ ร ๐ ร ๐ ร ๐ ร ๐ ร ๐ ร ๐ (๐ ร ๐)(๐ ร ๐ ร ๐)(๐ ร ๐ ร ๐ ร ๐ ร ๐)
A teacher wants to
assign 4 different task
to 4 students. In how
many possible ways
can she do it?
๐๐ท๐ = ๐! ๐ ๐ท ๐=๐! Given: (^) ๐ =๐
๐ ๐ท ๐=๐๐ ๐๐๐๐ Solution:
Find the number of
circular permutations
of seven dancers.
๐ท =( ๐ โ ๐)! ๐ท =(๐ โ ๐)! Given:
๐ท =๐๐๐ Solution: ๐ท =๐!
A committee of 5 people is to be chosen from 6 women and 7 men. Find the number of different committees that can be chosen (a) If there are no restrictions (b) If there are more men than women. Given: (^) ๐ =๐
Solution:
๐๐ ร ๐๐ ร ๐๐ ร ๐๐ ร ๐ ร๐
๐๐ ๐ช ๐=๐ , ๐๐๐
๐๐ ร ๐๐ ร ๐๐ ร ๐๐ ร ๐ ร๐
๐ ร ๐ ร ๐ ร๐ ร ๐
A committee of 5 people is to be chosen from 6 women and 7 men. Find the number of different committees that can be chosen (a) If there are no restrictions (b) If there are more men than women.
men women 5 4 3 2 0 1 2 3
Solution:
7 ๐ช 3 ร 6 ๐ช 2 =๐๐ ๐ ๐๐=๐๐๐ 7 ๐ช 5 ร 6 ๐ช 0 =๐๐ ๐ ๐=๐๐ 7 ๐ช 4 ร 6 ๐ช 1 =๐๐ ๐ ๐=๐๐๐ 7 ๐ช 3 ร 6 ๐ช 2 =๐๐ ๐ ๐๐=๐๐๐ ๐๐๐