Answer to Question #98264 in Combinatorics | Number Theory for Salmah

Question

The 10 students who completed a special flying course are waiting to see if they will be awarded the one distinctiin or the one merit award for their offers.
In how many ways can the two awards be given if the same student can recieve both awards?
Show full working and the table for the sample space!

Answer 1

Ways can the two awards be given if the same student can receive both awards (i.e repetition is allowed)

$$10\times10=100$$

$$1D1M, 1D2M, 1D3M, 1D4M,1D5M,$$ $$1D6M,1D7M,1D8M,1D9M,1D10M,$$ $$2D1M, 2D2M, 2D3M, 2D4M,2D5M,$$ $$2D6M,2D7M,2D8M,2D9M,2D10M,$$ $$3D1M, 3D2M, 3D3M, 3D4M,3D5M,$$ $$3D6M,3D7M,3D8M,3D9M,3D10M,$$ $$4D1M, 4D2M, 4D3M, 4D4M,4D5M,$$ $$4D6M,4D7M,4D8M,4D9M,4D10M,$$ $$5D1M, 5D2M, 5D3M, 5D4M,5D5M,$$ $$5D6M,5D7M,5D8M,5D9M,5D10M,$$ $$6D1M, 6D2M, 6D3M, 6D4M,6D5M,$$ $$6D6M,6D7M,6D8M,6D9M,6D10M,$$ $$7D1M, 7D2M, 7D3M, 7D4M,7D5M,$$ $$7D6M,7D7M,7D8M,7D9M,7D10M,$$ $$8D1M, 8D2M, 8D3M, 8D4M,8D5M,$$ $$8D6M,8D7M,8D8M,8D9M,8D10M,$$ $$9D1M, 9D2M, 9D3M, 9D4M,9D5M,$$ $$9D6M,9D7M, 9D8M,9D9M,9D10M,$$ $$10D1M, 10D2M, 10D3M, 10D4M,10D5M,$$ $$10D6M,10D7M, 10D8M,10D9M,10D10M.$$