To form the first group of three wolves with the male wolf included, we need to choose 2 additional female wolves from the 8 available female wolves.
The number of ways to choose 2 female wolves from 8 is calculated using the binomial coefficient, which is given by:
\[ \binom{n}{r} = \frac{n!}{r!(n - r)!} \]
In this case, \( n = 8 \) (the number of female wolves) and \( r = 2 \) (the number of female wolves we want to choose).
Calculating \(\binom{8}{2}\):
\[ \binom{8}{2} = \frac{8!}{2!(8 - 2)!} = \frac{8!}{2!6!} = \frac{8 \times 7}{2 \times 1} = \frac{56}{2} = 28 \]
Thus, there are 28 ways to choose 2 female wolves from the 8 available female wolves.
Since the male wolf is already included in the first group, the total number of ways to choose the first group of three wolves (1 male and 2 females) is \( 28 \).
Therefore, the answer is:
28 ways.
1 answer