Problem: what is the probability that when a hand o f 6 cards is drawn from a well shuffled deck of 52 cards , it contains 2 queen ?
Rationale: ncr = n ! / ( n - r ) ! r ! total number of possible hands = 52 c 6 52 c 6 = ( 52 ! ) / ( ( 52 - 6 ) ! × 6 ! ) 52 c 6 = 61075560 . number of hands with 2 queen and 4 non - queen cards = 4 c 2 × 48 c 4 4 c 2 = ( 4 ! ) / ( 2 ! × 2 ! ) = 6 . 48 c 4 = ( 48 ! ) / ( 44 ! × 4 ! ) = 3 × 47 × 46 × 45 = 291870 ( other 2 cards must be chosen from the rest 48 cards ) p ( 2 queen ) = ( 4 c 2 × 48 c 4 ) / 52 c 6 = 29187 / 1017926 c
annotated_formula: divide(multiply(choose(const_4, 2), choose(subtract(52, const_4), subtract(6, 2))), choose(52, 6))