The numbers 3, 4, 5, and 7 are written on separate pieces of paper and put into a hat. Two pieces of paper are drawn at the same time and the product of the numbers is recorded. Find the sample space.

the final sample space is { 12,15,20,21,28,35}

Step-by-step explanation:

the sample space is the set of possible outcomes of the experiment, then the possible products are

3*7 = 21

3*5 = 15

3*4 = 12

4*7 = 28

4*5 = 20

5*7 = 35

since the product of 2 numbers is commutative, then we do not count the other possible combinations

therefore the final sample space is { 12,15,20,21,28,35}

Note:

to check that we have all the products, the possible combinations are

C (4,2) = 4! / (4-2) !*2! = 3*2*1 = 6

since we have considered 6 products, we are sure that our result is correct