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stepladder [879]
3 years ago
7

A certain four​-cylinder combination lock has 50 numbers on it. to open​ it, you turn to a number on the first​ cylinder, then t

o 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
Mathematics
2 answers:
Kaylis [27]3 years ago
8 0
There are 230,300 combinations.

This is given by

_nC_r = _{50}C_4=\frac{50!}{46!4!} = 230,300
kumpel [21]3 years ago
7 0

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 .

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