Question

For the problem a) show how the permutation formula can be used to find the answer and b) write a sentence to explain the meaning of the answer for the situation.

To register for online banking services at a local credit union, you need to select a four-digit personal identification number, or pin code. The digits cannot be repeated. How many ways are there to arrange four digits out of the numerals 0 through 9 to create a code?

Answer 1

@imqwerty

Answer 2

1st we need to know how to find the number of ways in which we can do a task
According to Fundamental principle of counting-If an event \(A\) can occur in \(m\) different ways and event \(B\) can occur in \(n\) different ways. Then these events can occur in \(m \times n\) different ways in definite order.

So we have a 4 digit password
we need to find the number of ways in which we can password/make the password

okay so
so total ways will be-\(10 \times 9 \times 8 \times 7 =5040\)
so we have 5040 ways

we can also do it like this-

we need to select and arrange 4 numbers out of the given 10 numbers to make the pass
so the number of ways will be- \(^{10}P_4=5040\)