A certain four​-cylinder combination lock has 50 numbers on it. to open​ it, you turn to a number on the first​ cylinder, then to a second number on the second​ cylinder, and then to a third number on the third cylinder and so on until a four​-number lock combination has been affected. repetitions are​ allowed, and any of the 50 numbers can be used at each step to form the combination.​ (a) how many different lock combinations are​ there

Accepted Solution

There are 230,300 combinations.

This is given by

[tex]_nC_r = _{50}C_4=\frac{50!}{46!4!} = 230,300[/tex]