Question

The number of ways of selecting 4 cards of an ordinary pack of playing cards so that exactly 3 of them are of the same denomination is

Answer 1

Given :  4 cards to be selected  

To find : Number of ways exactly 3 of them are of the same denomination

Step-by-step explanation:

Exactly 3 cards of same denominations can be  

from 1 to 13  

so that  can be selected in ¹³C₁ = 13 ways

now 3 card to be selected from 4 cards of same denominations can be selected in ⁴C₃  = 4 ways

1  card can be selected in  ⁴⁸C₁  = 48 ways

Hence total number of Selection =   ¹³C₁  * ⁴C₃ *   ⁴⁸C₁  

13 * 4 * 48

= 52 * 48

= 2496

2496 ways of selecting 4 cards of an ordinary pack of playing cards so that exactly 3 of them are of the same denomination

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