<p>A standard deck of cards contains 52 cards. How many possible 5 card hands contain atleast 4 hearts?</p>
<p>.....I'm stumped</p>
<p>13 x 12 x 11 x 10 x 39= 669,240</p>
<p>13 for the 13 possible hearts
12 of the remaining 12
11 for the remaining hearts
10 for the remaining hearts
and 39 for the other non hearts.</p>
<p>can someone confirm if this is right?</p>
<p>your question is kind of vague.
copy the exact question on here, it would help. and answer choices? lol</p>
<p>Question asks "at least".
So answer is 13x12x11x10x48</p>
<p>the answer in the book is 29,172 but I can't figure out the soution</p>
<p>52 C 5 = 2598960 five card combinations</p>
<p>Well I don't know but there are more than 2 million combinations 52<em>51</em>50<em>49</em>48 yields around 311 million combinations so 13 times 12 times 11 times 10 times 48 sounds logical, but I don't know about order</p>
<p>Order does not matter. It asks for number of hands, not probability. My answer should be correct.</p>
<p>13C5 + (13C4) * 39 = 29172</p>
<p>The first part is the number of possible 5-heart hands, the next part is the number of 4-heart hands...</p>
<p>So I figured it out I was actually looking at permutations instead of combinations. So the total if you were to select all hearts is 13 choose 5 or 13<em>12</em>11<em>10</em>9/5! or 13<em>11</em>9. then 13 choose 4 = 13<em>11</em>5 (simplified) then you mutiply by 39 for every card that is not a heart and then you add the two together to get 13<em>11</em>(9+5*39) or 29172.</p>
<p>Hope that helps</p>
<p>fignewton writes: 13C5 + (13C4) * 39 = 29172</p>
<p>and is totally correct, but I (personally -- lots of people don't) like to express it like this (3rd line of my solution) because I find the consistency helps students understand:</p>
<h1>of hands with at least 4 hearts</h1>
<p>= [# of hands with exactly 5 hearts and 0 non-hearts] + [# of hands with exactly 4 hearts and exactly 1 non-heart]
= [13C5 * 39C0] + [13C4 * 39C1] <-- see all the unnecessary stuff I wrote? :)
= 29172</p>
<p>Writing the redundant combinations lets you "think" consistently I find.
There are 13 hearts and 39 non-hearts. So, for each situation (4 hearts; 5 hearts), just ask yourself, of the hearts, how many do you want AND of the non-hearts, how many do you want?</p>
<p>Thanks a lot! I really appreciate all the help guys.</p>