Fundamental counting principle6/17/2023 ![]() Question 3: Why is the counting principle important?Īnswer: The fundamental principles are the basic rules of mathematics that allows you to find the number of ways that a combination of events can occur. In simple words, it is the idea that if there are ways of doing something and there are ways of doing another thing and also there are ways of doing both actions. Question 2: State the basic counting principles?Īnswer: In basic counting, the rule of product or multiplication is the fundamental principle of counting. of possible outcomes of the experiment = 2 50 Every toss of the coin is independent of every other toss of the coin, since whenever you toss the coin there would be two possible outcomes with equal probability. What is the number of possible outcomes of this experiment?Īnswer : A coin toss has two possible outcomes: ‘A heads’ or ‘A tails’. This would ensure that everytime the event takes place, any of its outcomes are possible. If we conduct this event n number of times, then the number of outcomes of ‘n trials of the event’ will be, m nĬlearly, this is only valid when all the outcomes of the experiment/event E are independent of each other. Suppose we have an event E with ‘m’ possible outcomes. We must note that all the possible number of ways derived thus, all of them will represent the unique and distinct ways in which the event E will take place. with the respective number of ways given as n (P 1), n(P 2), n(P 3), n(P 4)….n(P n), then the number of ways in which P 1 and P 2 and …. Similarly, if there are several mutually independent events P 1, P 2, P 3, P 4……P n…etc. with the respective number of ways given as n (P 1), n(P 2), n(P 3), n(P 4)….n(P n), then the number of ways in which either P 1 and P 2 and …. In general, if there are several mutually exclusive events P 1, P 2, P 3, P 4……P n…etc. Generalisation of the Addition and the Product Rule Thus there are 15 different ways in which Jacob can buy a ping pong ball and a tennis ball from the sports shop. N(Jacob buys both one tennis ball and a ping-pong ball) = 5C 1 × 3C 1 = 5 3 = 15 ![]() ![]() N(Jacob buying one tennis ball and a ping-pong ball) = n(Jacob buys a ping pong ball) n(Jacob buys a tennis ball) Solution: Clearly the phenomenon of Jacob buying a ping pong ball is independent of the phenomenon of Jacob buying a tennis ball. ![]() In how many ways can Jacob buy a ping pong ball and a tennis ball? There is a total of five ping pong balls and 3 tennis balls available in the shop. Question: Jacob goes to a sports shop to buy a ping pong ball and a tennis ball. Let’s try and understand it with an example. This is The Multiplication Rule of Counting or The Fundamental Counting Principle. Then, the number of ways in which the event E can occur or the number of possible outcomes of the event E is given by: both event A and event B must occur (note the difference from the previously mentioned case). Let E be an event describing the situation in which either event A occurs, AND event B occur i.e. (We’ll show this physically through our solved example) one event’s outcome does not affect the other event’s outcome. In similarity to the events defined as in the Addition Rule, let us have two events namely A and B such that both are mutually independent of each other i.e. What is permutation? Learn here in detail. You can download Permutations and Combinations Cheat Sheet by clicking on the download button belowīrowse more Topics under Permutations And Combinations Thus there are 8 possible ways in which Jacob can buy a ball from the store, according to his specific wishes. Solution: n(Jacob buying a ball) = n(Jacob buys one ball from the amateur section) + n(Jacob buys one ball from the professional section) he can buy one ball from the amateur section OR one ball from the professional section? How many ways are possible in which he can buy a ball i.e. He wishes to choose one ball from the amateur section, which had a total of five balls or one ball from the professional section, which had a total of three balls. Question: Jacob goes to a shop to buy some ping pong balls. Let’s clarify our concepts with a suitable example. This is known as the Addition Rule of Counting. Let E be an event describing the situation in which either event A occurs, OR event B occurs. they have no outcome common to each other. Also, the events A and B are mutually exclusive events i.e. The number of ways in which event A can occur/the number of possible outcomes of event A is n(A) and similarly, for the event B, it is n(B).
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