Question

Se the following for problems 13 & 14. Three cards are drawn from a well-shuffled standard 52-card

Answer 1

Answer:

              $\bold{(13)\ \dfrac{11}{1105}=0.1\%}\\\\\\\bold{(14)\ \dfrac{4}{8575}=0.05\%}$

Step-by-step explanation:

(13)   Face cards are: Kings, Queens, and Jacks

There are 4 Kings, 4 Queens, and 4 Jacks in a standard deck of cards

$1st\ card\qquad \times \qquad 2nd\ card\qquad \times \qquad 3rd\ card\\\\\dfrac{\text{12 K, Q, J's}}{\text{52 total cards}}\times\dfrac{\text{11 K, Q, J's}}{\text{51 remaining cards}}\times \dfrac{\text{10 K, Q, J's}}{\text{50 remaining cards}}\\\\\\=\dfrac{12\times 11\times 10}{52\times 51 \times 50}=\dfrac{1320}{132,600}=\large\boxed{\dfrac{11}{1105}}$

(14)  There are 4 Aces and 4 Kings in a standard deck of cards

$1st\ card\qquad \times \qquad 2nd\ card\qquad \times \qquad 3rd\ card\\\\\dfrac{\text{4 Aces}}{\text{52 total cards}}\times\dfrac{\text{4 Kings}}{\text{51 remaining cards}}\times \dfrac{\text{3 remaining Kings}}{\text{50 remaining cards}}\\\\\\=\dfrac{4\times 4\times 3}{52\times 51 \times 50}=\dfrac{48}{132,600}=\large\boxed{\dfrac{4}{8575}}$