Question

How many permutations can be formed by sampling 5 things from 6 different things without replacement?

Answer 1

When selecting more than one item without replacement and order is important, it is called a Permutation. When order is not important, it is called a Combination.

The formula for a permutation is given by : n!/(n-r)!

here n = 6 and r = 5

thus answer = 6!/1! = 6!

Ans = 720

Answer 2

To calculate the number of permutations when sampling 5 things from 6 different things without replacement, we use the formula for permutations:

P(n, r) = n! / (n - r)!

Where: P(n, r) is the number of permutations of r things taken from a set of n things, n! is the factorial of n (n × (n - 1) × (n - 2) × ... × 3 × 2 × 1), and r is the number of things being sampled.

In this case, we have 6 different things (n = 6) and we are sampling 5 things (r = 5). Plugging these values into the formula:

P(6, 5) = 6! / (6 - 5)! = 6! / 1! = 6 × 5 × 4 × 3 × 2 × 1 / 1 = 720

Therefore, there are 720 different permutations that can be formed by sampling 5 things from 6 different things without replacement.