Want to Step Up Yo Being a math student, you might have faced many situations where combinations and permutations didn't enter your brains. Why don't you forget those times and start all over. Easier said than done, but it's better late than never to learn the puzzling concept of combination permutation. We will make it happen for you.
Learning the combination formula
Combination signifies selection. When you select or pick certain things (specific quantity) out of certain total things, the combination formula applies. Here, you do not have to follow the order in which the things have been picked by you.
The standard combination formula is given by C (n, r) = n! / r! (n - r)!, where n is number of total objects and r is number of objects that have selected out of n total objects. Let us take a problem for applying the combination formula.
Problem: A group of 12 students are lined up for their basketball-team selection. The coach has to select 6 out of 12 students to form the team. In how many ways can the coach select the students?
Solution: As per the given values, we can say that n = 12 and r = 6. Now, we can substitute these values in the combination formula.
C (12, 6) = 12! / 6! 6! = 924. Thus, there are total 924 ways of selecting the students.
Understanding the permutation formula
Permutation means arrangement. Here, when you select objects or things, the order in which you pick or select does matter. So, permutation signifies selection plus arrangement.
The standard permutation formula is P (n, r) = n! / (n - r)!, where n represents the total things out of which r things have been picked or selected by you. Let us work with a problem for applying the permutation formula.
Problem: You are given 5 alphabets. In a single turn, you can choose only 3 alphabets, so as to form a meaningful word. In how many ways can you do it?
Solution: Evidently, the rule of permutation applies here; the order in which you pick alphabets for forming words does matter. Therefore, going by the given values, we can easily say that here n = 5 and r = 3. Substituting these values in the permutations formula, as given below:
P (5, 3) = 5! / 2! = 60. Thus, you can form the words in 60 ways.
Logic of combination permutation
The concept of combination permutation gives you the ways in which you can perform a certain task. The main difference between them is the order. In permutation, you select plus arrange the objects (things) and in combination, you only select the things; which is why the order is important in permutation and negligible in combination.
Learning the combination formula
Combination signifies selection. When you select or pick certain things (specific quantity) out of certain total things, the combination formula applies. Here, you do not have to follow the order in which the things have been picked by you.
The standard combination formula is given by C (n, r) = n! / r! (n - r)!, where n is number of total objects and r is number of objects that have selected out of n total objects. Let us take a problem for applying the combination formula.
Problem: A group of 12 students are lined up for their basketball-team selection. The coach has to select 6 out of 12 students to form the team. In how many ways can the coach select the students?
Solution: As per the given values, we can say that n = 12 and r = 6. Now, we can substitute these values in the combination formula.
C (12, 6) = 12! / 6! 6! = 924. Thus, there are total 924 ways of selecting the students.
Understanding the permutation formula
Permutation means arrangement. Here, when you select objects or things, the order in which you pick or select does matter. So, permutation signifies selection plus arrangement.
The standard permutation formula is P (n, r) = n! / (n - r)!, where n represents the total things out of which r things have been picked or selected by you. Let us work with a problem for applying the permutation formula.
Problem: You are given 5 alphabets. In a single turn, you can choose only 3 alphabets, so as to form a meaningful word. In how many ways can you do it?
Solution: Evidently, the rule of permutation applies here; the order in which you pick alphabets for forming words does matter. Therefore, going by the given values, we can easily say that here n = 5 and r = 3. Substituting these values in the permutations formula, as given below:
P (5, 3) = 5! / 2! = 60. Thus, you can form the words in 60 ways.
Logic of combination permutation
The concept of combination permutation gives you the ways in which you can perform a certain task. The main difference between them is the order. In permutation, you select plus arrange the objects (things) and in combination, you only select the things; which is why the order is important in permutation and negligible in combination.