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MATHCOUNTS TOOLBOX Facts, Formulas and Tricks. Lesson 11: Permutations.

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Presentation on theme: "MATHCOUNTS TOOLBOX Facts, Formulas and Tricks. Lesson 11: Permutations."— Presentation transcript:

1 MATHCOUNTS TOOLBOX Facts, Formulas and Tricks

2 Lesson 11: Permutations

3 Consider the possible arrangements of the letters a, b, and c. List the outcomes in the sample space. If the order is important, then each arrangement is a permutation of the three letters

4 Outcomes in the sample space. abc acb bac bca cab cba There are six permutations.

5 Permutation Formula: Use when the item possibilities are all different. n: number of available items or choices r: the number of items to be selected Sometimes this formula is written: P(n,r).

6 If n = 5 and r = 2, what is the value of 5 P 2 ? The symbol 5 P 2 means the number of permutations of 5 items taken 2 at a time.

7 A permutation of 5 objects taken 2 at a time is equal to...

8 If n = 5 and r = 2, what is the value of 5 P 2 ? The symbol 5 P 2 means the number of permutations of 5 items taken 2 at a time. A permutation of 5 objects taken 2 at a time is equal to...

9 How many permutations are there for the letters in the word, BANANA? First, notice there are six total letters of which the A is repeated 3 times and the N is repeated 2 times. The number of permutations is equal to....

10 There are six letters in BANANA (6!). The A repeats three times (3!) and the N repeats two times (2!). There are 60 permutations.

11 How many permutations are there for the letters in the word, BANANA? First, notice there are six total letters of which the A is repeated 3 times and the N is repeated 2 times. The number of permutations is equal to.... There are six letters in BANANA (6!). The A repeats three times (3!) and the N repeats two times (2!). There are 60 permutations.

12 How many permutations are there for the letters in the word, HAPPY? Remember to ask yourself, how many total letters are there? How many letters are repeated? How many times is each letter repeated?

13 There are five letters in HAPPY (5!). The P repeats two times (2!). There are

14 How many permutations are there for the letters in the word, HAPPY? Remember to ask yourself, how many total letters are there? How many letters are repeated? How many times is each letter repeated? There are five letters in HAPPY (5!). The P repeats two times (2!). There are

15 1) Calculate the value of 7 P 3

16 A permutation of 7 objects taken 3 at a time is equal to...

17 1) Calculate the value of 7 P 3 A permutation of 7 objects taken 3 at a time is equal to...

18 2) Calculate the value of 9 P 4

19 A permutation of 9 objects taken 4 at a time is equal to...

20 2) Calculate the value of 9 P 4 A permutation of 9 objects taken 4 at a time is equal to...

21 How many permutations are there for the letters in the word, STATISTICS?

22 There are ten letters in STATISTICS (10!).

23 How many permutations are there for the letters in the word, STATISTICS? There are ten letters in STATISTICS (10!). The S repeats three times (3!), the T repeats three times (3!), and the I repeats two times (2!).

24 How many permutations are there for the letters in the word, STATISTICS? There are ten letters in STATISTICS (10!). The S repeats three times (3!), the T repeats three times (3!), and the I repeats two times (2!).

25 Fini!


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