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Formulae: Permutations & Combinations Video Lecture | General Aptitude for GATE - Mechanical Engineering
FAQs on Formulae: Permutations & Combinations Video Lecture - General Aptitude for GATE - Mechanical Engineering
| 1. What is the difference between permutations and combinations? |  |
Ans. Permutations and combinations are both mathematical concepts used to count the number of possible outcomes. The main difference between them lies in whether the order of the elements matters. In permutations, the order matters, while in combinations, the order does not matter. For example, if you have three items A, B, and C, the permutation ABC is different from CBA, but in combinations, ABC and CBA would be considered the same.
| 2. How do you calculate the number of permutations? | |
Ans. The number of permutations can be calculated using the formula:
nPr = n! / (n - r)!
Where n is the total number of items and r is the number of items taken at a time. The exclamation mark denotes factorial, which means multiplying a number by all the positive integers less than it. For example, 4! = 4 x 3 x 2 x 1 = 24.
| 3. What is the formula for combinations? | |
Ans. The formula for combinations is given by:
nCr = n! / (r! * (n - r)!)
Where n is the total number of items and r is the number of items taken at a time. Similar to permutations, the exclamation mark denotes factorial. The combination formula takes into account that the order of the elements does not matter.
| 4. How do permutations and combinations relate to probability? | |
Ans. Permutations and combinations are closely related to probability as they help calculate the number of possible outcomes in an event. In probability, permutations are used to calculate the number of ways an event can occur when the order matters, while combinations are used when the order does not matter. By knowing the total number of permutations or combinations, and the number of favorable outcomes, one can calculate the probability of an event occurring.
| 5. Can you provide a real-life example where permutations and combinations are used? | |
Ans. A real-life example where permutations and combinations are used is in lottery games. When you choose a set of numbers, the order in which the numbers are drawn does not matter, so combinations are used to calculate the odds of winning. On the other hand, if you are interested in the exact order in which the numbers are drawn, permutations would be relevant. Both permutations and combinations help determine the probability of winning a lottery prize.
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