Improve Article Save Article Like Article The term “combination” is thrown around loosely, and usually in the wrong way. Things like, “Hey, what’s the suitcase lock combination?” are said But what one really ought to be saying is “Hey, what’s the suitcase lock permutation?” So what’s the difference? And what exactly are a permutation and combination? They are two very different terms. Let’s learn about them in detail, PermutationA permutation is an act of arranging objects or given quantity maybe numbers from a group of objects or collection given in a particular order as per given conditions. Example – How many 2 letter words are there that can be formed by using the letters in the word LATE? Answer is 4P2 (pronounced as 4 p 2) = 4!/(4 – 2)! = 4!/(2)! = (4 × 3 × 2 × 1)/(2 × 1) = 24/2 = 12. The combination is the way of selecting the objects or given quantity maybe numbers from a group of objects or collection from a group of objects or collection, in such a way that the order of the objects does not matter. For example – how many groups of 2 people can be selected from 4 people? Answer – 4 C 2(pronounced as 4 C 2) = 4!/(4 – 2)!(2)! = 4!/(2)!(2)! = (4 × 3 × 2 × 1)/(2 × 1)(2 × 1) = 24/4 = 6. The formula for permutations and combinations
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Similar ProblemsQuestion 1: Find the number of committees of the size of 3 formed from 5 people. Answer:
Question 2: How many different committees of 3 members can be chosen out of 5 people in a group so that one particular person is always chosen? Answer:
Question 3: How many committees of 5 consisting of 3 men and 2 women can be formed from 8 men and 6 women? Answer:
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P(n,r) = n! / (n-r)!P(8,4) = 8! / (8-4)!P(8,4) = 8! / 4! P(8,4) = 1,680 ways |