Question

How many 6 digit different locker combinations are possible if no repeat numbers are allowed?

Answer 1

Since we are trying to find the number of sequences can be made without repetition, we are going to use a combination.

The formula for combinations is:

`_n C _k = (n!)/(k! (n - k)!)`

• 
  `n` is the total number of elements in the set
• 
  `k` is the number of those elements you are desiring

Since there are 10 total digits,
`n = 10` in this scenario. Since we are choosing 6 digits of the 10 for our sequence,
`k = 6` in this scenario. Thus, we are trying to find
`_(10) C _6`. This can be found as shown:

`_(10) C _6 = (10!)/(6! \cdot 4!) = (10 \cdot 9 \cdot 8 \cdot 7)/(4!) = (5040)/(24) = 210`

There are 210 total combinations.