Question

in order to conduct an experiment, 4 subjects are randomly selected from a group of 43 subjects. how many different groups of 4 subjects are possible?
the number of possible different groups is
(type a whole number.)

Explanation:

Step1: Identify the combination formula

The formula for combinations is \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n\) is the total number of items, and \(r\) is the number of items to be chosen. Here, \(n = 43\) and \(r=4\).

Step2: Substitute values into the formula

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Step3: Simplify the expression

Cancel out the \(39!\) terms. Then calculate \(\frac{43\times42\times41\times40}{4\times3\times2\times1}\).
\(43\times42\times41\times40 = 43\times42\times1640=43\times68880 = 2961840\)
\(4\times3\times2\times1=24\)
\(\frac{2961840}{24}=123410\)

Answer:

\(123410\)