A student has time to visit 3 of their 6 favorite colleges. How many different ways can the visits be arranged? 20 18 720 120
Question
A student has time to visit 3 of their 6 favorite colleges. How many different ways can the visits be arranged? 20 18 720 120
Solution
This is a problem of permutations. The student has 6 colleges to choose from and wants to visit 3 of them. The order in which the colleges are visited matters, so we use the formula for permutations:
P(n, r) = n! / (n-r)!
where n is the total number of options (6 colleges), r is the number of options chosen at a time (3 colleges), and "!" denotes factorial.
Step 1: Calculate n! = 6! = 65432*1 = 720
Step 2: Calculate (n-r)! = (6-3)! = 3! = 321 = 6
Step 3: Substitute these values into the formula: P(6, 3) = 720 / 6 = 120
So, there are 120 different ways the student can arrange visits to 3 of their 6 favorite colleges.
Similar Questions
There are 11 students on the tennis team. The coach selects 3 of them to go to a tennis clinic. In how many ways can he choose 3 of the 11 students?A.990B.165C.330D.55SUBMITarrow_backPREVIOUS
There are 10 students on the basketball team. The coach selects 3 of them to go to a basketball clinic. In how many ways can she choose 3 of the 10 students?A.210B.45C.720D.120
There are 6 seniors on student council. Two of them will be chosen to go to an all-district meeting. How many ways are there to choose the students who will go to the meeting?Decide if this is a permutation or a combination, and then find the number of ways to choose the students who go.A.Combination; number of ways = 15B.Permutation; number of ways = 15C.Combination; number of ways = 30D.Permutation; number of ways = 30
A teacher has to choose the maximum different groups of three students from a total of six students. Of these groups, in how many groups there will be included a particular student?Choices:- 6 8 10 12
There are 39 students in a class. The class teacher announced that the first 3 students who completes a given project within two days will be awarded. What are the possible number of ways the students will be awarded?39!36!3!36!3!39! 39!36!36!39! 39!39!36!36!
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.