Question

nine wolves, eight female and one male, are to be released into the wild three at a time. if the male wolf is to be in the first released group and order does not matter, in how many ways can the first group of three wolves be formed?
28 ways
36 ways
56 ways
84 ways

Explanation:

Step1: Identificar el problema

Es un problema de combinaciones.

Step2: Determinar los valores

Sabemos que el lobo macho ya está en el grupo. Necesitamos elegir 2 lobas de 8.

Step3: Aplicar la fórmula de combinaciones

La fórmula de combinaciones es $C(n,k)=\frac{n!}{k!(n - k)!}$, donde $n = 8$ (lobas) y $k=2$.
$C(8,2)=\frac{8!}{2!(8 - 2)!}=\frac{8!}{2!×6!}=\frac{8\times7\times6!}{2\times1\times6!}=28$.

Answer:

A. 28 ways