Answer
$_{52}C_1=52$
Work Step by Step
RECALL:
$_nC_r = \dfrac{n!}{r!(n-r)!}$
Use this definition to have:
$\require{cancel}
_{52}C_1=\dfrac{52!}{1!(52-1)!}
\\_{52}C_1=\dfrac{52!}{1(51!)}
\\_{52}C_1 = \dfrac{52(51!)}{(51!)}
\\_{52}C_1 = \dfrac{52\cancel{(51!)}}{\cancel{51!}}
\\_{52}C_1=52$
