Deck of Cards

Level pending

In a certain deck of cards, there are 100 100 cards. 10 10 cards are marked with stars, the remaining 90 90 are not marked. A set of 5 5 cards is chosen randomly from the deck. If the probability of the set containing no cards with stars is ( x z ) ( y z ) \dfrac{\dbinom{x}{z}}{\dbinom{y}{z}} , what is the value of x + y + z x+y+z ?

[The answer is under dispute. The answer need not be unique.]


The answer is 205.

Josh Speckman by Josh Speckman , 20, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Michael Mendrin
May 14, 2014

You're right, the solution is not unique. The more obvious one would have been

90 ! ( 90 − 5 ) ! ( 100 − 5 ) ! 100 ! \frac { 90! }{ (90-5)! } \frac { (100-5)! }{ 100! }

so that x+y+z = 195. It took a while to find another one, x=95, y=100, z=10,

yielding the same probability, so that x+y+z = 205.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...