View Discussion Improve Article Save Article Like Article View Discussion Improve Article Save Article Like Article Permutation is known as the process of organizing the group, body, or numbers in order, selecting the body or numbers from the set, is known as combinations in such a way that the order of the number does not matter. In mathematics, permutation is also known as the process of organizing a group in which all the members of a group are arranged into some sequence or order. The process of permuting is known as the repositioning of its components if the group is already arranged. Permutations take place, in almost every area of mathematics. They mostly appear when different commands on certain limited sets are considered. Permutation Formula In permutation r things are picked from a group of n things without any replacement. In this order of picking matter.
Combination A combination is a function of selecting the number from a set, such that (not like permutation) the order of choice doesn’t matter. In smaller cases, it is conceivable to count the number of combinations. The combination is known as the merging of n things taken k at a time without repetition. In combination, the order doesn’t matter you can select the items in any order. To those combinations in which re-occurrence is allowed, the terms k-selection or k-combination with replication are frequently used. Combination Formula In combination r things are picked from a set of n things and where the order of picking does not matter.
Solution:
Similar Questions Question 1: In how many ways can the letters be arranged so that all the vowels came together word is CORPORATION? Solution:
Question 2: In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged such that the vowels must always come together? Solution:
Question 3: In How many ways the letters of the word RAINBOW be arranged in which vowels are never together? Solution:
Exercise :: Permutation and Combination - General Questions
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Exercise :: Permutation and Combination - General Questions
120 Questions 480 Marks 120 Mins
Concept:
Calculation: The word CORPORATION has 11 letters out of which 6 are consonants (CRPRTN) and 5 are vowels (OOAIO). Considering the objects of the same type, the number of arrangements of these vowels will be \(\rm \dfrac{5!}{3!}\) = 20. Since, the vowels have to be together, we can say that we have to arrange the groups (C), (R), (P), (R), (T), (N) and (OOAIO) among themselves. Considering the objects of the same type, this can be done in \(\rm \dfrac{7!}{2!}\) = 2520 ways. And, total number of arrangements of all the letters = [Number of arrangements of (C), (R), (P), (R), (T), (N) and (OOAIO)] × [Number of arrangements of (OOAIO)] = 20 × 2520 = 50400. India’s #1 Learning Platform Start Complete Exam Preparation
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