More on Permutations

1. More on Permutations

2. Topics in this Section Permutation with Repetition Circular Permutations Bracelet Permutations

3. Permutation with Repetition How many ways are there to arrange the letters in the word GRIFFIN? =1260 GRIFFIN How many different signals can be made by displaying five flags all at a time, on a flagpole, if two are red, two are black, and one is blue? =30 RRBBL

4. Permutation with Repetition How many different signals can be made by displaying five flags all at a time, on a flagpole, if three are red, one is black, and one is blue? =20 RRRBL In how many ways can three red, four blue, and two green pens be distributed among nine students if each student receives one pen? =1260 RRRBBBBGG

5. Permutation with Repetition How many five-digit integers can be formed using 1 and 2 twice, and three only once? =30 11223 How many ways are there to arrange the letters in the word ALGEBRA? =2520 AALGEBR

6. B A C G D F E Circular Permutations (n – 1)! BUT… How many ways are there to arrange seven chairs around a round table? X A B D E F G

7. Circular Permutations (n – 1)! BUT… How many ways are there to arrange five people around a circle if John and Bill have to sit next to each other? A B C D J X B C D J B J C D 12

8. Another Permutation with Restriction Find all the permutations of the letters A, B, C, D, E, F if the consonants must remain together. B C D F A E 144

9. One More Permutation with Restriction How many ways can three boys and three girls be arranged In a circle if the girls MUST remain next to each other? X B1 B2 B3 G1 G2 G3 36

10. Bracelet Permutations How many ways are there to arrange six beads on a bracelet? How many ways are there to arrange eight charms on a bracelet?