# 3 cards are drawn from a standard 52 playing cards deck. Find the odds of drawing just two spades?

3 cards are drawn from a standard 52 playing cards deck. Find the odds of drawing just two spades?

• Questions are typically answered in as fast as 30 minutes

### Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

svartmaleJ
There're 3 ways to draw exactly 2 hearts when 3 cards are drawn:
The 1st and 2nd cards are spades. probability of $$\displaystyle\frac{{13}}{{52}}\times\frac{{12}}{{51}}\times\frac{{39}}{{50}}={0.046}$$
The 1st and 3rd cards are spades. probability of $$\displaystyle\frac{{13}}{{52}}\times\frac{{39}}{{51}}\times\frac{{12}}{{50}}={0.046}$$
The 2nd and 3rd cards are spades. probability of $$\displaystyle\frac{{39}}{{52}}\times\frac{{13}}{{51}}\times\frac{{12}}{{50}}={0.046}$$
The odds of drawing 2 spades are 0.046=4.6%