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:

$_n C _k = \dfrac{n!}{k! (n - k)!}$

• $n$ 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:

$_{10} C _6 = \dfrac{10!}{6! \cdot 4!} = \dfrac{10 \cdot 9 \cdot 8 \cdot 7}{4!} = \dfrac{5040}{24} = 210$

There are 210 total combinations.