The first six triangular numbers (1,3,6,10,15, 21) are printed once each on one side of a card. the cards are placed face down and mixed. choose two cards at random, and let x be the sum of the two numbers. construct the probability distribution for this random variable x.

See description below.

To complete your table, you could create a tree diagram to show all of the different possibilities of the the event. There would be 30 outcomes because you are drawing from 6 cards then 5 cards.

6 x 5 = 30

Be careful when you complete your chart, because some of the numbers may be repeated. Be sure to combine them. 

Okay so it will be 1123