4 cards are drawn from a well-shuffled deck of 52 cards. What is the probability of obtaining 3 diamonds and one spade?
Let, the 4 cards are drawn from deck of 52 cards.
The total number of ways to draw 4 cards from 52 cards is 52 C 4 .
There are 52 cards in deck in which 13 diamonds and 13 spades.
The number of ways drawn 3 diamonds and one spade is 13 C 3 × 13 C 1 .
The probability of obtaining three diamonds and one spade.
P ( 3 diamond and 1 spade ) = 13 C 3 × 13 C 1 52 C 4 = 13 ! 3 ! ( 10 ) ! × 13 ! 1 ! ( 12 ) ! 52 ! 4 ! ( 48 ) ! = 13 ! 3 ! ( 10 ) ! × 13 ! ( 12 ) ! × 4 ! ( 48 ) ! 52 ! = 286 20825
Thus, the probability is 286 20825 .
Let, the
The total number of ways to draw
There are
The number of ways drawn 3 diamonds and one spade is
The probability of obtaining three diamonds and one spade.
Thus, the probability is
