The topic of discussion on a television news program was a decision made by a three-judge panel chosen at random from a certain circuit of judges. The guest on the program stated, "because there are 35 judges in the circuit, there are 3500 different combinations of three-judge panels." Is this true? If not, what is the correct number?
Jeanine Baker makes floral arrangements. She has 18 different cut flowers and plans to use 6 of them. How many different selections of the 6 flowers are possible?
A state lottery game requires that you pick 5 different numbers from 1 to 73. If you pick 4 of the 5 numbers correctly, you win $250,000. In how many ways can you pick exactly 4 of the 5 winning numbers without regard to order?