![]() ![]() For the first letter, we have 5 possible choices out of A, B, C, D, and E. Let us break down the question into parts. ![]() \( \Longrightarrow \) There are 60 different arrangements of these letters that can be made. \( \Longrightarrow\ _nP_r =\ _5P_3 = 60 \) applying our formula \( \Longrightarrow r = 3 \) we are choosing 3 letters \( \Longrightarrow n = 5 \) there are 5 letters Let us first determine our \( n \) and \( r \): We will solve this question in two separate ways. If the possible letters are A, B, C, D and E, how many different arrangements of these letters can be made if no letter is used more than once? When dealing with more complex problems, we use the following formula to calculate permutations:Ī football match ticket number begins with three letters. The arrangements of ACB and ABC would be considered as two different permutations. Suppose you need to arrange the letters A, C, and B. \( \Longrightarrow \) There are 10 ways in which Katya can choose 3 different cookies from the jar.Īs mentioned in the introduction to this guide, permutations are the different arrangements you can make from a set when order matters. \( \Longrightarrow\ _nC_r =\ _5C_3 = 10 \) applying our formula \( \Longrightarrow r = 3 \) we are choosing 3 cookies \( \Longrightarrow n = 5 \) there are 5 cookies Since order was not included as a restriction, we see that this is a combination question. We must first determine what type of question we are dealing with. In how many ways can Katya choose 3 different cookies from the jar? Katya has a jar with 5 different kinds of cookies. Where \( n \) represents the total number of items, and \( r \) represents the number of items being chosen at a time. When dealing with more complex problems, we use the following formula to calculate combinations: ![]() The arrangements of ACB and ABC would be considered as one combination. As introduced above, combinations are the different arrangements you can make from a set when order does not matter. ![]()
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