reto wrote:
From the following list of five question stems, how many are permutations questions and how many are combinations questions?
I. How many ways can ten students arrange themselves in a row of ten seats?
II. How many groups of students can attend a conference if there are ten students and four passes to attend the conference?
III. How many subcommittees of four are possible from a committee of 12 people?
IV. How many ways can Karl arrange his twelve books on a shelf?
V. How many seating arrangements are possible for six couples sitting around a circular table?
A. 1 permutation, 4 combination
B. 2 permutation, 3 combination
C. 3 permutation, 2 combination
D. 4 permutation, 1 combination
E. All five are permutation questions
Could somone please A.) comment each question on the list with the answer to the question and B.) explain how one easily recognises that the question is a permutation or combination problem.
Here are the keywords:
Combination - Selection
Permutation - Arrangement
I. How many ways can ten students arrange themselves in a row of ten seats?
Arrange themselves - Permutation
II. How many groups of students can attend a conference if there are ten students and four passes to attend the conference?
Out of 10,
select 4 for 4 passes - Combination
III. How many subcommittees of four are possible from a committee of 12 people?
Out of 12,
select 4 - Combination
IV. How many ways can Karl arrange his twelve books on a shelf?
Arrange 12 - Permutation
V. How many seating arrangements are possible for six couples sitting around a circular table?
Arrange six couples - Permutation
Often, questions have both permutation and combination. e.g.
How many different results are possible for a race of 10 students if the results give ranks of first, second and third?
Out of 10 students, you need to
select 3 - Combination
and then
arrange the three into first, second third positions - Permutation