Permutation Under Certain Conditions
Permutation Under Certain Conditions
Permutation
All the possible ways the things can be arranged by using some or all the things are called permutation. Thus each of the arrangements which can be made by taking some or all number of things is called a permutation.
The various ways in which the three things can be arranged by taking two at a time are known as the permutation of three things takes two at a time.
The permutations which can be made by taking the letters a, b and c by taking two at a time are 6 i.e., ab, bc, ac, ba, cb and ca. Each of these presenting a different arrangement of two letters. These six arrangements are called permutations of three things takes two at a time.
Permutation Under Certain Conditions
Permutations where certain conditions are applied fall in this category. The conditions may be in terms of not using all the items or, a particular item should occur in each and every permutation.
Number of permutations of n different things, taken r at a time, when a particular things is to be always included in each arrangement
.
For Example: A team of 3 cars is to be formed from 8 cars in which one car is always included, then possible arrangement is
Number of permutations of n different things taken all at a time, when m specified things always come together is
For example, The total ways in which the letters of word DISCOVER can be arranged in which all vowels are always together is
Here the total letters are = 8
In a class of 10 students there are 3 girls. In how many ways can they be arranged in a row such that no two of the three girls are consecutive ? | |||
| Right Option : C | |||
| View Explanation | |||
A team of 5 boys is to be formed from 8 boys in which one boy is always included, what will be the total number of all possible arrangement? | |||
| Right Option : B | |||
| View Explanation | |||
All the five letters of the word TABLE are arranged to form different words without repeating any letter in any word. The words so formed are, then arranged as in dictionary. What will be the position of the word TABEL in that sequence ? | |||
| Right Option : B | |||
| View Explanation | |||
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