Question

a bakery offers 6 types of cookies. if a customer wants to buy a box of 4 different cookies, how many different boxes can be made?
$_{6}c_{4} = ?$
hint:
$_{n}c_{r} = \frac{_{n}p_{r}}{r!}$

Explanation:

Step1: Recall combination formula

The combination formula is $C(n, r) = \frac{n!}{r!(n-r)!}$, where $n=6$, $r=4$.

Step2: Calculate factorials

$6! = 6×5×4×3×2×1 = 720$, $4! = 24$, $(6-4)! = 2! = 2$.

Step3: Compute the value

$C(6,4) = \frac{720}{24×2} = \frac{720}{48} = 15$.

Answer:

15