Question

If from a deck of 52 cards,4 cards are selected and 1 card of it should be spade and another should be heart,in how many ways can these cards be selected? a)13^2*50C2 b)52C4 c)26*50C2 d)13C4

Answer 1

a)13^2*50C2 is the correct answer

Answer 2

Answer:

The answer is option  ( a ) 13^2 * ⁵⁰C₂

Step-by-step explanation:

Since we know,

In a deck of 52 cards, there are 13 spades and 13 hearts

According to question,

4 cards are to selected and 1 card should be spade and another should be heart

Let A be event of selecting a card of spade, that is,

We need to select 1 card out of 13 cards of spade

Number of ways of doing so = ¹³C₁ = 13

Let B be event of selecting a card of heart

Similarly as above,

Number of ways of doing so = ¹³C₁ = 13

Now number of cards left = 52 - 2 = 52 ( Since two cards are already taken out )

Number of ways of selecting the left out 2 cards = ⁵⁰C₂

So,

In all number of ways these cards can be selected = 13 * 13 * ⁵⁰C₂

= 13^2 * ⁵⁰C₂

Hence,

The answer is option  ( a ) 13^2 * ⁵⁰C₂