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Forming Numbers: Permutations & Combinations- 4 Video Lecture - Mechanical Engineering
FAQs on Forming Numbers: Permutations & Combinations- 4 Video Lecture - Mechanical Engineering
| 1. What is the difference between permutations and combinations? |  |
Ans. Permutations and combinations are both methods used to count the number of possible outcomes. The main difference is that permutations consider the order of the elements, while combinations do not. In permutations, the order matters, whereas in combinations, the order does not matter.
| 2. How do we calculate the number of permutations? | |
Ans. To calculate the number of permutations, we use the formula nPr = n! / (n - r)!, where n is the total number of items and r is the number of items chosen. The exclamation mark (!) denotes factorial, which means multiplying all positive integers from 1 to the given number.
| 3. What is the formula for combinations? | |
Ans. The formula for combinations is nCr = n! / (r!(n - r)!), where n is the total number of items and r is the number of items chosen. Similar to permutations, the exclamation mark (!) represents factorial.
| 4. Can you provide an example of permutations and combinations? | |
Ans. Sure! Let's say you have 5 different colors of balls (red, blue, green, yellow, and orange) and you want to arrange them in a row.
- Example of permutations: If you want to arrange all 5 balls in a specific order, that would be a permutation. The number of permutations would be 5! = 5 x 4 x 3 x 2 x 1 = 120.
- Example of combinations: If you want to select 3 balls from the 5 available colors, without considering the order, that would be a combination. The number of combinations would be 5C3 = 5! / (3!(5-3)!) = 10.
| 5. How are permutations and combinations useful in real-life scenarios? | |
Ans. Permutations and combinations have various applications in real-life scenarios. They are used in probability calculations, statistics, genetics, computer science, and many other fields. For example, when dealing with lottery numbers, card games, or password combinations, permutations and combinations are used to determine the total number of possible outcomes and to calculate the probability of specific events occurring.
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