Question

Question 2 4 cards are drawn from a well-shuffled deck of 52 cards. What is the probability of obtaining 3 diamonds and one spade?

Class X1 - Maths -Probability Page 408

Answer 1

Total number of ways selecting 4 cards out of 52 cards n(S ) = ⁵²C₄

number of ways getting 3 diamonds out of 13 = ¹³C₃
number of ways getting one spade out of 13 = ¹³C₁
so, total number of favourable outcomes n(E ) =
event obtaining 3 diamonds and one spade = ¹³C₃ × ¹³C₁

now, P(E ) = n(E)/n(S)
= ¹³C₃ × ¹³C₁ / ⁵²C₄