Question

One card is dealt to each of four people. In how many ways could all the cards be hearts or non- face cards?

Answer 1

There are 13 hearfs in a deck

Number of ways of choosing 4 cards from 13 hearts = ¹³C₄ = 715

There are 3 types of face cards (King, Queen, Jack) in a deck and 4 cards of each face type

Thus there are total 3 x 4 = 12 face cards

And there are 52 - 12 = 40 non-face cards

Number of ways in which 4 cards can be chosen from 40 non-face cards = = ⁴⁰C₄ = 91390

Total number of ways that all the cards are hearts or non- face cards = 715 + 91390 = 92105

Total number of ways that all the cards are hearts or non- face cards =

--------------------------------------------------------------------------------------------------------------------
If you are satisfied with the solution, kindly give a thumbs up.