# Cards

royalchicken
Posers and Puzzles 26 May '03 22:45
1. royalchicken
CHAOS GHOST!!!
26 May '03 22:45
Given a standard, 52-card deck, how many combinations of five cards consist of at least three spades and exactly two cards of equal rank?
2. richjohnson
TANSTAAFL
27 May '03 18:381 edit
Originally posted by royalchicken
Given a standard, 52-card deck, how many combinations of five cards consist of at least three spades and exactly two cards of equal rank?
31086?
3. royalchicken
CHAOS GHOST!!!
27 May '03 20:22
Maybe, maybe not. What is your reasoning?
4. richjohnson
TANSTAAFL
27 May '03 23:00
Originally posted by royalchicken
Maybe, maybe not. What is your reasoning?
(1). # of 5-card combos wherein the pair are not one of the 3 spades = (# of distinct 3-spade combos) x (# of distinct non-spade pairs that dont match one of the spades + # of single spade pairs) = 66 x ((39 - 9) + (9x3)) = 3762

(2). # of combos wherein one of the pair is one of the 3 spades = (# of distinct 3-spade combos) x (# of possibilities for the 4th card for a given set of 3 spades) x (# of possibilities for the 5th card) = 66 x 9 x (48 - (2 (so that the 5th card doesn't match the pair) + 3 + 3 (so that the 5th card doesn't match either of the other two cards)) = 23760.

(1) + (2) = 27522.

(my original calculations didn't account for the possible matching of the pair with one of the spades)
5. royalchicken
CHAOS GHOST!!!
28 May '03 01:471 edit
I get 27522......Good job ðŸ˜€! (My method was different though.)