Question

in order to conduct an experiment, 5 subjects are randomly selected from a group of 32 subjects. how many different groups of 5 subjects are possible?

the number of possible different groups is
(type a whole number)

Explanation:

Identify the counting method

Using the Combinatorics knowledge point
We need to select a group of 5 subjects from a pool of 32. Since the order of selection within the group does not matter, we use combinations.

Apply the combination formula

Using the Combinatorics knowledge point

$$ C(n, r) = \frac{n!}{r!(n-r)!} $$

Here, \(n = 32\) and \(r = 5\).

Calculate the value

Using the Combinatorics knowledge point

$$ C(32, 5) = \frac{32 \times 31 \times 30 \times 29 \times 28}{5 \times 4 \times 3 \times 2 \times 1} $$

$$ C(32, 5) = \frac{24,165,120}{120} = 201,376 $$

Answer:

In order to conduct an experiment, 5 subjects are randomly selected from a group of 32 subjects. How many different groups of 5 subjects are possible?

The number of possible different groups is <blank>201376</blank>
(Type a whole number)