Question

enter the correct answer a student is packing a lunch and can choose 2 fruits out of these 4: apples, bananas, oranges, and grapes. how many different fruit combinations can they pack? \\( _4c_2 = \boxed{?} \\) hint: \\( _nc_r = \frac{_np_r}{r!} \\)

Explanation:

Step1: Recall combination formula

Combination formula: $\binom{n}{k} = \frac{n!}{k!(n-k)!}$ where $n=4$, $k=2$.

Step2: Calculate factorials

$4! = 4×3×2×1 = 24$, $2! = 2×1 = 2$, $(4-2)! = 2! = 2$.

Step3: Compute combination

$\binom{4}{2} = \frac{24}{2×2} = 6$.

Answer:

6