In the last few minutes of a diving team practice, there is time for 2 of the 6 divers to line up and do a particular dive. How many sequences of 2 divers are possible?
Question
In the last few minutes of a diving team practice, there is time for 2 of the 6 divers to line up and do a particular dive. How many sequences of 2 divers are possible?
Solution
The problem can be solved using the concept of permutations in combinatorics.
A permutation is an arrangement of objects in a specific order. The number of permutations of n objects taken r at a time is given by the formula:
P(n, r) = n! / (n-r)!
where "!" denotes factorial, which is the product of all positive integers up to that number.
In this case, we have 6 divers (n=6) and we want to know how many sequences are possible for 2 divers (r=2).
So, we plug these values into the formula:
P(6, 2) = 6! / (6-2)!
= 720 / 24
= 30
So, there are 30 different sequences of 2 divers possible.
Similar Questions
Lena has 6 errands to run this week, and she would like to take care of 2 of them today. In how many sequences could she run any 2 of the errands today? sequencesSubmit
A TV station is going to air a movie marathon with 8 movies. It will consist of 2 science fiction movies and 6 horror movies. The horror movies will be aired later in the evening. So, all of the horror movies will be aired last (after both of the science fiction movies). In how many ways can the station air the movie marathon?
In a race with eight swimmers, how many ways can the swimmers finish first, second and third?
One day, Wet Shark was given an array . As always, he started playing with its subsequences.When you came to know about this habit, you presented him a task of finding all pairs of subsequences, , which satisfies all of the following constraints. We will represent a pair of subsequence as and and must be of same length, i.e., .Please help Wet Shark determine how many possible subsequences and can exist. Because the number of choices may be big, output your answer modulo .Note:Two segments are different if there's exists at least one index such that element is present in exactly one of them.Both subsequences can overlap each other.Subsequences do not necessarily have to be distinctInput FormatThe first line consists of 3 space-separated integers , , , where denotes the length of the original array, , and and are as defined above.The next line contains space-separated integers, , representing the elements of .ConstraintsOutput FormatOutput total number of pairs of subsequences, , satisfying the above conditions. As the number can be large, output it's modulo
There were 9 students running in a race. How many different arrangements of first, second, and third place are possible?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.