Question

questions: 4,5 and 6

A theoretical analysis of this problem would consider all of the possible ways to distribute the four babies to the four mothers. Let 1234 mean that the first baby went to the first mother, the second baby to the second mother, the third baby to the third mother, and the fourth baby to the fourth mother. In this scenario all four mothers get the correct baby. As another example, 1243 would mean that the first two mothers got the right baby, but the third and fourth mothers had their babies switched. All of the possibilities are listed here:

            1234                1243                1324                1342                1423                1432

            2134                2143                2314                2341                2413                2431

            3124                3142                3214                3241                3412                3421

            4123                4132                4213                4231                4312                4321

4) How many possibilities are there for returning the four babies to their mothers?

5) For each of these possibilities, indicate how many mothers get the correct baby. Write the number beside the possibility in the above list.

6) In how many possibilities do all four mothers get the correct baby? What percentage is this?

Answer 1

a) Total. 4x3x2x1 = 24 possibilities are there.

b) All of the possibilities and number of mothers getting correct baby in each case are listed here:

1234 - 4

1243 - 2

1324 - 2

1342 - 1

1423 - 1

1432 - 2

2134 - 2

2143 -0

2314 - 1

2341 - 0

2413 - 0

2431 - 1

3124 - 1

3142 - 0

3214 - 2

3241 - 1

3412 - 0

3421 -0

4123 - 0

4132 - 1

4213 - 1

4231 -2

4312 - 0

4321 - 0

c) In only one case all four mothers get their correct babies.

Percentage of this = (1/24 )x 100= 4.166%