Question

From a finite population of 1 point N=7, the number of samples of size n=3 that can be drawn is

Answer 1

The number of samples of size
`\( n = 3 \)` that can be drawn from a finite population of
`\( N = 7 \) is \( 35 \).`

Step-by-step explanation:

In combinatorics, the number of ways to choose r elements from a set of n distinct elements is given by the binomial coefficient \
`( \binom{n}{r} \),`also known as "n choose r." This is calculated as
`\( (n!)/(r!(n-r)!) \), where \( n! \) denotes the factorial of \( n \),` which is the product of all positive integers up to
`\( n \).`

In this case, we are interested in the number of ways to choose
`\( 3 \) elements from a population of \( 7 \)`. Using the binomial coefficient formula:

`\[ \binom{7}{3} = (7!)/(3!(7-3)!) \]`

Simplifying the factorials:

`\[ \binom{7}{3} = (7 * 6 * 5)/(3 * 2 * 1) \]`

Which equals
`\( 35 \). Therefore, there are \( 35 \)` different combinations or samples of size
`\( 3 \) that can be drawn from a finite population of \( 7 \).`