Probability of NOT getting dealt a room card in a 3-person game of Clue.

Question

What is the probability of being dealt a hand of 6 cards that contains no "room" cards? i.e. all of the cards in your hand are either a weapon or a suspect (out of a total deck of 8 room cards + 5 weapon cards + 5 suspect cards = 18 cards)

Answer 1

Total number of cards $= 18$

Total number of ways to pick 6 cards out of 18 $={18\choose 6}$

Number of weapon/suspect cards $= 5+5=10$

Number of ways to pick 6 cards out of 10 $={10\choose 6}$

$$P={{10\choose 6}\over {18\choose 6}}=0.01131=1.131\%$$