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

Solution:

The number of ways of drawing r different objects from n different objects is ⁿCᵣ.

The number of ways of drawing 4 cards from 52 cards = ⁵²C₄.

We know that in a deck of 52 cards, there are 13 diamonds and 13 spades.

Therefore, the number of ways of drawing 3 diamonds and one spade = ¹³C₃ × ¹³C₁

Thus, the probability of obtaining 3 diamonds and one spade = ¹³C₃ × ¹³C₁ / ⁵²C₄

NCERT Solutions Class 11 Maths Chapter 16 Exercise ME 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?

Solution:

4 cards are drawn from a well-shuffled deck of 52 cards. Then the probability of obtaining 3 diamonds and one spade is ¹³C₃ × ¹³C₁ / ⁵²C₄