Question

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

Answer 1

There are 230,300 combinations.

This is given by

$_nC_r = _{50}C_4=\frac{50!}{46!4!} = 230,300$

Answer 2

A certain four​-cylinder combination lock has 50 numbers on it.

It is a four cylinder combination lock

Each cylinder has 50 numbers

So we have to choose 4 numbers for 4 cylinders

_____ , ______ , ______, _____

you turn to a number on the first​ cylinder

We have 50 numbers so we have 50 combinations

__50___ , ______ , ______, _____

Repetitions are allowed so we do the same for remaining three

50 , 50 , 50 , 50

50 * 50 * 50* 50 = 6250000

There are 6250000 different lock combinations .