A certain lock has five tumblers, and each tumbler can assume six positions. How many different possibilities are there?

Question

I am doing most of my questions for my homework on probability and I Do not know how solve any of them 

Answer 1

6⁵=6*6*6*6*6=7776 different possibilities

suppose there were only 2 tumblers

tumbler 1 can be in position 1,2,3,4,5, or 6

tumbler 2 can be in position 1,2,3,4,5, or 6

tumbler 1 can be in position 1 and tumbler 2 can be in position 1

tumbler 1 can be in position 1 and tumbler 2 can be in position 2

tumbler 1 can be in position 1 and tumbler 2 can be in position 3

and so on...

all the possibilities are:

11,12,13,14,15,16

21,22,23,24,25,26

31,32,33,34,35,36

41,42,43,44,45,46

51,52,53,54,55,56

61,62,63,64,65,66

there are 6²=6*6=36 possibilities

if there were 3 tumblers, each of the 36 possibilities can be combined with position 1,2,3,4,5, or 6 for a total of 6*36=216 possibilities

if there were 4 tumblers you would have 216*6=1296 possibilities

Answer 2

The first tumbler has 6 options, as well as the second-fifth tumber.

So, you are multiplying 6x6x6x6x6 or 6⁵ = 7776

 

This is assuming that numbers can repeat.