Question

Cards are drawn one by one without replacement from a well shuffled pack of $52$ cards. Then, the probability that a face card (jack, queen or king) will appear for the first time on the third card is equal to

Answer 1

Total No of ways of choosing three cards from the deck$={}^{52}{C}_3$

As the face card is taken $1^{st}$ time in three takes, the first 2 takes cannot be face cards.\

So, No of possibilities for $1^{st}$ 2 takes$={}^{52-12}{C}_2={}^{40}{C}_2$

and as the third take is a face card,

No of possibility for all takes$={}^{40}{C}_2{\times }^{12}{C}_1\times 2$

$Probability=\frac{Nooffavourablepossibilities}{Totalnoofways}=\frac{{}^{40}{C}_2\times {}^{12}{C}_1}{{}^{52}{C}_3}.2=\frac{72}{17\times 5}=\frac{72}{85}$