Counting techniques

Counting techniques

1. Counting techniques are mathematical strategies used in probability and statistics that allow to determine the total number of results that can be from making combinations within a set or sets of objects. These types of techniques are used when it is practically impossible or too heavy to manually make combinations of different elements and know how many of them are possible

2. are the following five, although not the only ones, each with its own particularities and used according to the requirements to know how many combinations of sets of objects are possible.

3. The most used are combinations and permutations, it should be noted that these techniques provide us with information in all possible ways in which a given event occurs.

   • As we have mentioned before, the combinations are the arrangements where we don't care about the position of the elements. Its formula is as follows: nCr=n!/(n-r)!r!

4. 4. Permutations with repetition When you want to know the number of permutations in a set of objects, some of which are the same, you proceed to do the following:

   • When you want to know the number of permutations in a set of objects, some of which are the same, proceed as follows: Taking into account that n are the available elements, some of them are repeated. All n elements are selected.

5. 3. Permutations Before understanding how to make permutations, it is It is important to understand the difference between a combination and a permutation. A combination is an arrangement of elements whose order does not it is important or does not change the final result. On the other hand, in a permutation, there would be an arrangement of several elements in which it is it is important to take into account your order or position.

   • A combination would be an arrangement of elements in which we are not interested in position occupied by each of them. A permutation, on the other hand, would be a arrangement of elements in which we are interested in the position occupied by each one of them.

6. aking into account that n are the available elements, some of them repeated. All n elements are selected. The following formula applies: = n!/n1!n2!... nk!

   • When you want to know the number of permutations in a set of objects, some of which are the same, proceed as follows: Taking into account that n are the available elements, some of them are repeated. All n elements are selected.

7. 2. Additive principle In this case, instead of multiplying the alternatives for each event, what happens is that the various ways in which they can occur are added together. This means that if the first activity can occur in M forms, the second of N and the third L, then, according to this principle, it would be M + N + L.

   • Esto significa que si la primerIn this case, instead of multiplying the alternatives for each event, what happens is that the different ways in which they can occur are added together. This means that if the first activity can occur in M forms, the second in N and the third in L, then, according to this principle, it would be M + N + L.

8. The most used are combinations and permutations, it should be noted that these techniques provide us with information in all possible ways in which a given event occurs.

   • In combinations, unlike what happened with permutations, the order of the elements is not important. The formula to apply is as follows: nCr = n! / (Nr)! R!

9. Counting techniques are mathematical strategies used in probability and statistics that allow to determine the total number of results that can be from making combinations within a set or sets of objects. These types of techniques are used when it is practically impossible or to

   • it is used when the action is sequential, that is, it is composed of events that occur in an orderly manner, such as the construction of a house, the choice of dance steps in a disco or the order that will be followed to prepare. a cake. ta.

10. are the following five, although not the only ones, each with its own particularities and used according to the requirements to know how many combinations of sets of objects are possible.

    • This principle is used when the action is sequential, that is, it is composed of events that occur in an orderly manner, such as the construction of a house,

11. 3. Permutations Before understanding how to make permutations, it is It is important to understand the difference between a combination and a permutation. A combination is an arrangement of elements whose order does not it is important or does not change the final result.

    • When you want to know the number of permutations in a set of objects, some of which are the same, proceed as follows: Taking into account that n are the available elements, some of them are repeated. All n elements are selected. The following formula applies: = n! / N1! N2! Nk!

12. 2. Additive principle In this case, instead of multiplying the alternatives for each event, what happens is that the various ways in which they can occur are added together. This means that if the first activity can occur in M forms, the second of N and the third L, then, according to this principle, it would be M + N + L

13. aking into account that n are the available elements, some of them repeated. All n elements are selected. The following formula applies: = n!/n1!n2!... nk!

    • r otro lado, en una permutación, habría una disposición de varios elementos en los que es importante tener en cuenta su orden o posición. En las permutaciones, hay n número de elementos diferentes y se selecciona un número de ellos, que sería r. La fórmula que se utilizaría sería la siguiente: nPr = n! / (Nr)!

14. 4. Permutations with repetition When you want to know the number of permutations in a set of objects, some of which are the same, you proceed to do the following:

    • Cuando desee saber el número de permutaciones en un conjunto de objetos, algunos de los cuales son iguales, proceda de la siguiente manera: Teniendo en cuenta que n son los elementos disponibles, algunos de ellos se repiten. Se seleccionan todos los elementos n.

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