Preston invites a friend over to play board games. If he and his friend have 4 games to choose from, how many sequences of 2 board games are possible?
Question
Preston invites a friend over to play board games. If he and his friend have 4 games to choose from, how many sequences of 2 board games are possible?
Solution
To solve this problem, we need to use the concept of permutations. A permutation is an arrangement of objects in a specific order. The order of arrangement of the object is very important.
Step 1: Identify the total number of games. In this case, it is 4.
Step 2: Identify the number of games to be chosen at a time. In this case, it is 2.
Step 3: Use the formula for permutations when order matters, which is nPr = n! / (n-r)!. Here, n is the total number of games and r is the number of games to be chosen at a time.
Step 4: Substitute the values into the formula. So, 4P2 = 4! / (4-2)! = 4321 / 21 = 12.
So, there are 12 different sequences of 2 board games that Preston and his friend can play.
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