Hello friends,Previously we have discussed about what is calculus and today we are going to discuss a very interesting topic “discrete mathematics” which includes many topics of algebra like permutations, combinations, probability etc and falls under CBSE Board Syllabus. Discrete mathematics deals with the study of structures and curves which are not continuous or do not vary smoothly and is also very useful to solve math questions. For example study of sets is also included in discrete mathematics and we all know that a set is a well defined collection of objects which is nicely constructed for a particular interval or condition. Such kind of finite studies are involved in discrete mathematics. permutations and combinations is the another topic included in discrete mathematics which also refers to the finite calculations. Friends, discrete mathematics covers many topics of mathematics. Here we are going to discuss in detail about a very important topic of discrete mathematics which is called permutations. Now let’s start with the definition of permutation. Friends, permutations refer to the different arrangements of a number of things. Basically study of permutations can be helpful to obtain the following calculations (want to Learn more about Permutations ,click here),
1. To find the number of ways in which a task can be performed
2. To find the number of words with or without meaning that can be formed by using some or all of the letters of alphabets
3. To find the arrangement of ‘n’ things selected from ‘m’ different things
4. To form the different numbers of different digits by using ‘n’ digits from a set of ‘m’ different digits
Friends calculation of permutations involves the method of factorial which is a very helpful and essential tool in the study of algebra. Factorial of a number n is written as n! and is defined by the following formula
N! = n.(n-1).(n-2).(n-3)……3.2.1
For more clear understanding of factorial let’s take an example to find the factorial of 5.
5! = 5.4.3.2.1 = 120 Friends, this is how the factorial of any number can be calculated. Now let’s have a look on factorials of few initial numbers which are generally used in the calculations of permutations. Students are advised to learn the value of these basic factorials directly
1! = 1.
2! = 2.1 = 2
3! = 3.2.1 = 6
4! = 4.3.2.1 = 24
5! = 5.4.3.2.1 = 120
6! = 6.5.4.3.2.1 = 720
Friends, in permutations the number of arrangement of r things taken from n things at a time can be calculated by an important formula npr = n!/(n-r)!. Let's take few examples of permutations to understand this
Example: find the number of words that can be formed by 4 different letters of alphabets by taking 2 at a time without repetition of lattés.
This problem can be easily solved by using above formula as we have to form the words by taking 2 letters out of 4 we can find it by 4p2 = 4!/(4-2)! = 4!/2! = (4.3.2.1)/(2.1) = 12. Now we can say that 12 words with or without meaning can be formed.
Friends this is how we can proceed to solve the problems of permutations and if anyone want to know about De Morgans law then they can refer to internet and text books for understanding it more precisely.Read more maths topics of different grades such as Binomial Property in the next session here.
1. To find the number of ways in which a task can be performed
2. To find the number of words with or without meaning that can be formed by using some or all of the letters of alphabets
3. To find the arrangement of ‘n’ things selected from ‘m’ different things
4. To form the different numbers of different digits by using ‘n’ digits from a set of ‘m’ different digits
Friends calculation of permutations involves the method of factorial which is a very helpful and essential tool in the study of algebra. Factorial of a number n is written as n! and is defined by the following formula
N! = n.(n-1).(n-2).(n-3)……3.2.1
For more clear understanding of factorial let’s take an example to find the factorial of 5.
5! = 5.4.3.2.1 = 120 Friends, this is how the factorial of any number can be calculated. Now let’s have a look on factorials of few initial numbers which are generally used in the calculations of permutations. Students are advised to learn the value of these basic factorials directly
1! = 1.
2! = 2.1 = 2
3! = 3.2.1 = 6
4! = 4.3.2.1 = 24
5! = 5.4.3.2.1 = 120
6! = 6.5.4.3.2.1 = 720
Friends, in permutations the number of arrangement of r things taken from n things at a time can be calculated by an important formula npr = n!/(n-r)!. Let's take few examples of permutations to understand this
Example: find the number of words that can be formed by 4 different letters of alphabets by taking 2 at a time without repetition of lattés.
This problem can be easily solved by using above formula as we have to form the words by taking 2 letters out of 4 we can find it by 4p2 = 4!/(4-2)! = 4!/2! = (4.3.2.1)/(2.1) = 12. Now we can say that 12 words with or without meaning can be formed.
Friends this is how we can proceed to solve the problems of permutations and if anyone want to know about De Morgans law then they can refer to internet and text books for understanding it more precisely.Read more maths topics of different grades such as Binomial Property in the next session here.
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