Some children gather and exchange presents.
Another person other than the person who brought a present should bring it home.
How many ways of method of exchanging presents are there in the case of the following number of children?
(1) When exchanging by three persons.
(2) When exchanging by four persons.
(3) When exchanging by five persons.
Answer
(1) 2 ways
(2) 9 ways
(3) 44 ways
Solution
(1) Assume three children to be A, B, and C. Arrange as shown in a table below, there are two ways at all.
(2) When B brings the present of A home, it is arranged as in a table below and there are three ways.
Since it becomes three ways, respectively also when C and D bring the present of A home, there are 3 × 3 = 9 ways in all.
(3) When B brings the present of A home, it is arranged as in a table below and there are three 2 + 3 × 3 = 11 ways.
Since it becomes 11 ways, respectively also when C, D, and E bring the present of A home, there are 11 × 4 = 44 ways in all.
Another person other than the person who brought a present should bring it home.
How many ways of method of exchanging presents are there in the case of the following number of children?
(1) When exchanging by three persons.
(2) When exchanging by four persons.
(3) When exchanging by five persons.
Answer
(1) 2 ways
(2) 9 ways
(3) 44 ways
Solution
(1) Assume three children to be A, B, and C. Arrange as shown in a table below, there are two ways at all.
(2) When B brings the present of A home, it is arranged as in a table below and there are three ways.
Since it becomes three ways, respectively also when C and D bring the present of A home, there are 3 × 3 = 9 ways in all.
(3) When B brings the present of A home, it is arranged as in a table below and there are three 2 + 3 × 3 = 11 ways.
Since it becomes 11 ways, respectively also when C, D, and E bring the present of A home, there are 11 × 4 = 44 ways in all.
