Question

Alan is arranging 3 different stuffed toys in a row on a shelf. Create a sample space for the arrangement of a teddy bear (T), a kitten (K), and an elephant (E). (10 points)

Answer 1

Answer with explanation:

Number of toys in a shelf which we have to arrange in a row = 3= [Teddy Bear (T)+ A Kitten (K) +An Elephant (E)]

We have to arrange these toys in a row.

⇒Total number of Arrangement when there are three things in all and order of arrangement is Important we will apply the concept of Permutation.

           $_{3}^{3}\textrm{P}=\frac{3!}{(3-3)!}=3!\\\\=3 \times 2 \times 1\\\\=6$

Sample Space=(a)→T K E,(b)→T E K,(c)→K TE,(d)→K ET,(e)→E KT,(f)→E T K

Answer 2

Okay, so let's make a sample space where in one section, one toy is the leader of each group for as many possibilities as there are.

T K E
T E K
K E T
K T E
E T K
E K T

There are 6 possibilities, and so each arrangement has a 1 over 6 chance of being used.