A sequence where order distinguishes one sequence of things from another order o

Question

A sequence where order distinguishes one sequence of things from another order of the same things is called a permutation. Suppose we have things a, b, and c. Drawing without replacement 3 times produces the permutations {abc, acb, bac, bca, cab, and cba}. We see 3 things have 6 permutations or orders.

Let's generalize. For a sequence of n things drawn from N things without replacement, there are N ways the 1st draw occurs. For each of the N outcomes of 1st draw, there are N-1 ways the 2nd draw can occur. So, for 2 draws, there are N x (N - 1) possible permutations. Continuing, there are N x (N-1) x (N-2) permutations for 3 draws.

In general, it's N x (N - 1) x (N - 2) x . . . x (N - n +1) = N! / (N - n)! , or using Excel functions, =PERMUT( N, n)

! is read factorial

Example: 6! = 6 x 5 x 4 x 3 x 2 x 1

How many permutations can be formed by sampling 4 things from 8 different things without replacement?

THERE IS AN EXAMPLE WITH THE SAME QUESTION BUT I AM NOT UNDERSTANDING. I NEED A STEP BY STEP ANSWER PLEASE. THANK YOU!

Explanation / Answer

We have 8 different things. We need to sample (choose) 4 things and wnat to know in how many ways this can be possible.

Initially, there are 8 ways to select the 1st thing.

Now, after choosing 1 element, 7 things remains. So, there are 7 ways to select the 2nd thing.

Now, after choosing 2 elements, 6 things remains. So, there are 6 ways to select the 3rd thing.

Now, after choosing 3 elements, 5 things remains. So, there are 5 ways to select the 4th thing.

So, total number of ways (permutations) to sample (choose) 4 things from 8 different things

= 8 * 7 * 6 * 5 = 1680

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