Probability & Statistics (53 of 62) Permutations and Combinations - Example 18 By Michel van Biezen

Summary:

1. Introduction to the Problem: The lecturer introduces a complex example involving the formation of a six-letter word using a combination of consonants and vowels with specific restrictions.

2. Permutations and Combinations: The problem requires combining the concepts of permutations and combinations to determine the total number of possible permutations for the given scenario.

3. Calculation Process: The lecturer explains that the total number of permutations for a six-letter word, where order matters, is given by $�!$, where $�$ represents the number of letters.

4. Consideration of Consonants and Vowels: Since there are six consonants and five vowels available, the calculation involves selecting four consonants and two vowels from the respective sets.

5. Formula for Total Permutations: The total number of permutations is calculated by multiplying the permutations of consonants and vowels by the factorial of six (representing the total number of letters in the word).

6. Simplification of the Equation: The lecturer simplifies the equation by reducing factorials and performing arithmetic operations to obtain a final expression for the total number of permutations.

7. Final Result: After simplification, the lecturer arrives at the total number of permutations, which is 108,000. This represents the number of distinct six-letter words that can be formed using the specified criteria.

8. Conclusion: The lecturer concludes by emphasizing the importance of understanding permutations and combinations in solving complex probability problems, illustrating the process through the example discussed.