Question

Three cards are drawn at random from an ordinary pack, find the chance that they will consist of a knave, a queen, and a king.

Answer 1

Hint: Determine how many knaves (jacks), kings and queens are present in a deck of cards.

Complete step-by-step answer:
Total cards = 52
$ \Rightarrow $Total ways of drawing three cards = ${}^{52}{C_3}$
Total no of king = 4
Total no of queen = 4
Total no of knave = 4
Ways of drawing a king = ${}^4{C_1}$
Ways of drawing a queen = ${}^4{C_1}$
Ways of drawing a knave = ${}^4{C_1}$
$ \Rightarrow $ Favorable ways = ${}^4{C_1} \times {}^4{C_1} \times {}^4{C_1}$
Probability of drawing one king, one knave and a queen is
=$\dfrac{{Favorable{\text{ }}ways}}{{Total{\text{ }}ways}} = \dfrac{{{}^4{C_1} \times {}^4{C_1} \times {}^4{C_1}}}{{{}^{52}{C_3}}} = \dfrac{{4 \times 4 \times 4}}{{\dfrac{{52!}}{{49! \times 3!}}}}$
Therefore, Probability = $\dfrac{{64 \times 3 \times 2}}{{52 \times 51 \times 50}} = \dfrac{{16}}{{5525}}$
So, this is your required answer.

Note: In this type of question find out favorable ways and total ways, then divide them you will get your required probability.