Answer:
C. 15
Step-by-step explanation:
The number of ways to choose k elements from a set of n elements is given by the formula for combinations:
[tex]C(n,k) = \dfrac{n!}{k!(n-k)!}[/tex]
Where:
n is the total number of elements (6 dogs in this case)
k is the number of elements to choose (2 dogs in this case)
"!" denotes factorial
Plugging in n = 6, k =2 we get
[tex]C(6,2) = \dfrac{6!}{2!(6-2)!}\\\\=\dfrac{6!}{2!\;4!}\\\\\\= \dfrac{6 * 5 * 4 * 3 * 2* 1}{(2*1 )(4*3*2*1)}\\\\= \dfrac{30}{2}\\\\= 15[/tex]
Therefore, the dog trainer can choose 2 dogs from the kennel of 6 in 15 ways.
