Question

. from a deck of 52 cards, 4 cards are selected so as to include at least 1 spade card. in how many ways this can be done?

Answer 1

52/4=13 .13 ways the cards can be done

Answer 2

Answer:

There are 188474 ways to select 4 cards so as to include at least 1 spade card.

Step-by-step explanation:

Total cards = 52

No. of cards to be drawn = 4

So, total no. of ways of selecting 4 cards = $^{52}C_4$

No. of spades = 13

So, Remaining cards excluding spades = 52-13=39

So, No.of ways of selecting 4 cards with no spade = $^{39}C_4$

So, No. of ways of selecting 4 cards so as to include at least 1 spade card:

=  $^{52}C_4-^{39}C_4$

=  $\frac{52!}{4!(52-4)!}-\frac{39!}{4!(39-4)!}$

=  $188474$

Hence there are 188474 ways to select 4 cards so as to include at least 1 spade card.