![]() ![]() Hence, total number of games played= \(^8C_2\)=28 matches.Now, we only have to find the number of ways of selecting 2 teams from 8 teams. Thus, for each match to happen we must select 2 teams only and in this case, the arrangement will not matter.Ĭan you observe we arrived at the keyword SELECT by dissecting the given information carefully and making meaningful inferences?.The match between team A and team B is same as the match between team B and team A.We know that each game is played between two teams. Let us visualize the information given in the question and see if we can identify the type of the question. When we cannot find any keyword to identify whether the question is combination type or permutation type then we need to visualize the information provided to us in the question stem.This question does not include the important keywords then how should we solve this question? What is the total number of games played in the league? Q- There are 8 teams in a certain league and each team plays with the other teams exactly once. Let us understand this with the help of some examples. ![]() So, how do we determine whether the question is a combination question or a permutation question? Visualizing the scenario when keywords are not presentĪt times, you can get a question that implicitly uses the application of permutation and combination. Number of unique signals= \(^4C_3\) * 3! = 4*3! = 24ġ- Look for the important keyword- arrangements, ordered ways, and unique to identify the permutation question.Ģ- The number of ways to arrange ‘r’ things from ‘n’ things = \(^nP_r\).ģ- An arrangement question can also be solved by first choosing ‘r’ things among ‘n’ things and then arranging all the ‘r’ things.We can first select 3 different flags and then we can arrange them. Hence, number of unique signals= \(^4P_3\) = 24.Thus, we only have to apply \(^nP_r\) formula to arrive at the answer.Notice the keyword, UNIQUE, in the question. Now, per our understanding, the formula to select ‘r’ things from ‘n’ things, is \(^nC_r\), which is equal to \(\frac\)= 6 words. Therefore, we can infer that the keyword select is used for a combination question. In all the above cases, the selection of 2 players is same as the combination of 2 players only. Let us list all the cases in which a doubles team can be formed.Ĭan you notice the keyword- “SELECT”, in all the cases? Now, instead of solving this manually, let us apply the keyword approach to solve this question. Thus, we can have only 3 doubles teams from 3 players. Let us understand the concept of combination by solving example 1- “ From 3 players, A, B, and C, how many doubles team can be formed?”įrom 3 players A, B, and C, the teams of 2-players can be: This simple example clearly shows that the understanding of combination and permutation can help to decide when arrangement matters and when selection matters. ![]() But, in the second case, the arrangement of the letters can give us two different words. O Thus, in the first case, arrangement of the “team members” does not affect the team composition. ![]()
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