Exploring Permutations and Combinations in Code Assignments and Arrangements
This section delves into permutations and combinations, illustrating the principles through practical examples. We explore how many four-letter codes the FBI can create with and without letter repetition. Additionally, we cover how to line up 6 people and evaluate various permutation expressions like P(6,4) and P(40,4). The discussion then shifts to combinations, showcasing how to list combinations of colors and calculate values such as C(4,3) and C(40,4). Lastly, we consider arrangements of letters in the word ALEGBRA and vertical flag arrangements.
Exploring Permutations and Combinations in Code Assignments and Arrangements
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Presentation Transcript
Section 10.2 Permutations and Combinations
If the FBI assigned four-letter codes to various operations, such as operation ERRT, (notice that repetition of letters is allowed), how many codes are possible?
Suppose the FBI for their codes decided they did not want any letters repeated in their four letter codes. How many different four letter codes are there without repetition?
Evaluate: (a) P(6,4) (b) P(7, 2) (c) P(40, 4)
If you have a group of four people that each have a different birthday, how many possible ways could this occur?
List all the combinations of the 4 colors, red, green, yellow and blue taken 3 at a time. What is C(4, 3)?
Find the value of each expression. (a) C(4, 2) (b) C(5, 2) (c) C(n, n) (d) C(n, 0) (e) C(40, 4)
How many different committees of 4 people can be formed from a pool of 8 people? How many ways can a committee consisting of 3 boys and 2 girls be formed if there are 7 boys and 10 girls eligible to serve on the committee?
How many different words (real or imaginary) can be formed using all the letters in the word ALEGBRA?
How many different vertical arrangements are there of 10 flags if 5 are white, 4 are blue and 2 are red?
