how many 3 - card hands can be dealt from a standard deck of 52 cards?\n$_{n}c_{r}=\frac{n!}{r!(n - r)!}$
how many 3 - card hands can be dealt from a standard deck of 52 cards?\n$_{n}c_{r}=\frac{n!}{r!(n - r)!}$
Answer
Answer:
22100
Explanation:
Step1: Identify n and r values
n = 52, r = 3
Step2: Calculate factorial values
n!=52!=52×51×50×...×1, r!=3!=3×2×1, (n - r)!=(52 - 3)!=49!=49×48×...×1
Step3: Apply combination formula
${n}C{r}=\frac{n!}{r!(n - r)!}=\frac{52!}{3!(52 - 3)!}=\frac{52\times51\times50\times49!}{3\times2\times1\times49!}$
Step4: Simplify the expression
$\frac{52\times51\times50}{3\times2\times1}=\frac{132600}{6}=22100$