Question

question 6
1 pts
in how many ways can 6 students be selected from a group of 28 students to represent a school in the inter school essay competition?

Explanation:

Step1: Identify the problem type

This is a combination problem since the order of selecting students does not matter. The formula for combinations is \( C(n, k)=\frac{n!}{k!(n - k)!} \), where \( n = 28 \) (total number of students) and \( k=6 \) (number of students to be selected).

Step2: Calculate factorial values

First, recall that \( n!=n\times(n - 1)\times\cdots\times1 \). So we need to calculate \( 28! \), \( 6! \), and \( (28 - 6)!=22! \). The combination formula can be simplified as \( C(28,6)=\frac{28!}{6!×22!}=\frac{28\times27\times26\times25\times24\times23\times22!}{6!×22!} \). The \( 22! \) terms cancel out.

Step3: Compute the numerator and denominator

Calculate the numerator: \( 28\times27\times26\times25\times24\times23 \)
\( 28\times27 = 756 \)
\( 756\times26=19656 \)
\( 19656\times25 = 491400 \)
\( 491400\times24=11793600 \)
\( 11793600\times23 = 271252800 \)

Denominator: \( 6!=6\times5\times4\times3\times2\times1 = 720 \)

Step4: Divide numerator by denominator

\( C(28,6)=\frac{271252800}{720}=376740 \)

Answer:

376740