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Combination and Permutation In grade 10 3rd quarter mathematics topic

1. What is permutation? A Permutation is an arrangement of items in a particular order. Notice, ORDER MATTERS! 1  

2. OBSERVE THE TWO PROBLEMs. In how many ways can 3 students be chosen from 10 members of the group? In how many ways can tops 1, 2, and 3 be chosen from the 10 members of the group? 2 Which of the two problems involves arrangements? Which among the problem is a permutation, and why? How about the other one? Is it also a permutation? If not, what is it? The other one is called a combination. How would you define a combination?

3. Combinations A combination is an arrangement of an objects with no repetitions and the order is NOT important. 3  

4. STATE WHETHER EACH OF THE FOLLOWING IS A COMBINATION OR A PERMUTATION Permutation 4 Arrangement of 10 people in a row. A committee of 5 persons will be chosen from a group of 7 persons. A group of 45 people are going to run a race. The top three runners earn gold, silver and bronze metals. A team of 8 basketball players needs to choose a captain and co-captain. A hand of 13 cards having exactly 10 spades drawn from a deck of cards. Combination Permutation Permutation Combination

5. STATE WHETHER EACH OF THE FOLLOWING IS A COMBINATION OR A PERMUTATION Combination 5 6. There are 45 applicants for three Computer Programmer positions. 7. There are 110 people at a meeting. They each shake hands with everyone else. 8. Arrangement of 8 people at round table. 9. Number of 4 different digits that can be formed from 6 different digits. 10. Number of circles determined by 10 points, no three of which are collinear. Combination Permutation Permutation Combination

6. Evaluate the following.   6   =3 ways =15ways =84ways =70 ways =5 ways

7. Evaluate the following. In how many ways can a principal choose 3 of their 30 teachers to attend a conference abroad? Six officers of the Mathematics Club are in a conference room. If each one shakes hands with each of the others once, how many handshakes are possible? How many committee of 4 persons can be chosen from a group of 10 persons? 4. In how many ways can a committee of 5 person be chosen from 7 single ladies and 9 men? 7   4,060 ways 15 ways 210 ways 4,368 ways

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