Question

Five cards are chosen at random from a pack of $52$ cards. Then the probability that at least one face card is chosen, is

• A. $1-\frac{{}^{40}{C}_5}{{}^{52}{C}_5}$
• B. $1-\frac{{}^{12}{C}_5}{{}^{52}{C}_5}$
• C. $1-\frac{{}^{13}{C}_5}{{}^{52}{C}_5}$
• D. $1-\frac{{}^{39}{C}_5}{{}^{52}{C}_5}$

Answer 1

The correct option is A $1-\frac{{}^{40}{C}_5}{{}^{52}{C}_5}$

Choosing $5$ cards from a pack of $52$ cards
Total possible outcomes, $n\left(S\right)={}^{52}{C}_5$
and number of ways getting no face cards $={}^{40}{C}_5$
Let event $A=$ choosing at least one face card
$P\left(A\right)=1-P\left(A^c\right)=1-\frac{{}^{40}{C}_5}{{}^{52}{C}_5}$