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Sagot :
Since, there are 08 students in the class, among 02 of them should be selected as the best students in the class. In 28 different ways this can be done.
Use the formula of combinations given as ⁿ[tex]C_{r}[/tex] to find the numbers of possible ways to select r things out of a total of n things. Let n be the total number of students in the class and r as the number of students required to be selected as best students in the class. Now, use the formula
ⁿ[tex]C_{r}[/tex] = [tex]\frac{r!}{(n- r)!}[/tex] to simplify the expression .
Given that a class has 8 students in which 2 students will be selected for a best students in the class. .
Therefore, n = 08 and r = 02, substituting these values in the formula we get,
Number of possible ways of selection = ⁿ [tex]C_{r}[/tex] = ⁸C₂
Now,
Number of possible ways of selection = [tex]\frac{8!}{2! ( 8 - 2)!}[/tex]
Or, Number of possible ways of selection = [tex]\frac{8!}{2! 6!}[/tex]
Solving further,
Number of possible ways of selection = 8 × 7× 6!/ 2× 1 ×6!
Number of possible ways of selection = 4 × 7 = 28
Hence, the total number of ways to select the required number of students is 28.
Learn more about Combinations:
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