# Math/Probability

I need help with the following problem:

A brighe hand is made up of the 13 cards from a deck of 52. What is the probability of a hand chosen at random containing 6 of one suit, 5 off another, and 2 of another?

THe first card can be anything.
It seems to me that the probabality is this:
13*4/52 *12/51*11/50*10/49*9/48*8/47 *
13/46*12/45*11/44*10/43*9/42*
13/41*12/40

check my thinking.

I presume, D, you know the formula for calculating n-choose-x, where you have n things and need to choose x of them. = n!/(x!*(n-x)!)

So, lets start with the easy part, the denominator. It is 52-choose-13 -- the total of combinations of 13 cards from a deck of 52.

Now for the numerator. Of the 4 suits, one has 6 cards, one has 5, one has 2 and one has 0. How many permutations does this represent? The answer is n! or 4*3*2*1 = 24.

Now then, for the first suit, there are 13 cards in a suit, you need 6 -- so 13-choose-6. For the second suit its 13-choose-5, for the third its 13-choose-2.
So the numerator is 24 * (13-C-6) * (13-C-5) * (13-C-2).

check my thinking.

This may or may not agree with the other answers posted. It was provided by my son, who is an actuary and runs the website www.wizardofodds.com. He makes his living doing this sort of thing.

There are 24 ways to arrange the suits (4 possible suits for the long one, 3 for the medium, and 2 for the short suit).

There are 13!/(6!*7!) ways to pick 6 ranks out of 13 for the long suit.

There are 13!/(5!*8!) ways to pick 5 ranks out of 13 for the medium suit.

There are 13!/(2!*11!) ways to pick 2 ranks out of 13 for the short suit.

So the total number of combinations fitting the criteria is 4134297024.

The total number of all ways to pick 13 cards out of 52 is 52!/(13!*39!) = 635013559600

So the probability is 4134297024/635013559600 = 0.006510565

Your son's method and my posted method are the same. Your post goes further by actually showing the calculations.

Thanks. I see tnat now that your method is the same. I requested mu son's help last night before any answers were posted, and thought it would be a shame not to use his answer.

Thanks everyone! I've been stressing over this and it really helps seeing the different explanations.

how do i do probability trees when using replacement

fyunoeht ncqklmy kavyfrgp qrvfhig efcdnbvp fexc ijzwaq

fyunoeht ncqklmy kavyfrgp qrvfhig efcdnbvp fexc ijzwaq

1. 👍 0
2. 👎 0
3. 👁 100

## Similar Questions

1. ### Math-Geometry

Find the angle that the hr hands and the mins hand made when it at 10:00:45.67 so it 10olock 00 min and 45.67 sec and find the angles Show works it one of those clocks problem -thanks We're asked "Find the angle that the hr hands

asked by Bob on September 16, 2006
2. ### English

1. On the one hand they want to go abroad, but on the other hand they want to save more money. 2. On the one hand they like playing ping-pong, but on the other hand they want to go back home early. 3. On the one hand they want to

asked by rfvv on June 23, 2015
3. ### English

Does anyone know of something that people without a hand would need, something that would be useful to them in their daily lives or chores that they do? (Anything other than a fake hand or products that are already made).

asked by Amy~ on May 29, 2010
4. ### Physics

I have tried to solve this problem in multiple ways, but i keep getting it wrong please help A 48.0 {\rm kg} ice skater spins about a vertical axis through her body with her arms horizontally outstretched, making 1.50 turns each

asked by Mark on March 3, 2008
5. ### English

1. She held out her hand. 2. She extended her hand. --------- Are both the same? Can we use some other expressions instead of 'held out'? 3. It's been such a long time. 4. It's been so lone a time. --------------------------- What

asked by rfvv on August 22, 2014
6. ### Physics

A tower clock has an hour hand 2.70 m long with a mass of 60.o kg, and a minute hand 4.50 m long with a mass of 100 kg. Calculate the total rotational kinetic energy of the two hands about the axis of rotation. Sol: I know that Kr

asked by Anderson on April 18, 2007
7. ### Algebra Question

I did a problem and used the substitution method and it took me forever to solve by hand. Is there a shorter way to show how this problem was done. The problem was x+y+z=7,x-y+2z=7,2x+y+3z=15 The final answer came out to be x=4

asked by mike on December 18, 2009
8. ### math

it is now 2.00 pm and 15 minutes, what fraction of a whole turn did the minute hand make? what size of the angle in degrees made by the minute hand?

asked by luren on November 29, 2016
9. ### English

1. He raised his right hand a little. 2. He raised his right hand a bit. 3. He raised his right hand slightly. 4. He raised his right hand a lot. 5. He raised his right hand much. 6. He raised his right hand a little. 7. He raised

asked by rfvv on September 15, 2015
10. ### Algebra 2

Two days ago "Steve" helped me with this problem. I am grateful to him. I didn't get it and asked for him to help me again. He showed it to me again, but I needed more steps shown. Then I think he was finished for tutoring for the

asked by Bart on January 12, 2013

More Similar Questions