Question

Please justify answer, this is for a mathematical proofs class.

2. Determine the number of ways one can pick two cards from a standard 52-card deck, so that the first card is a spade and the second card is not an Ace.

Answer 1

Solution terc we haue to cletermine, the number of Pick tuoo Cards feom stundard the first card is a Spule ways one Can 52 Carrel dece i So that and Seconcd card is not an Ace For That two Ceuses make we first cord is a Ace ot spude Cuse Ci then this Case in henee Second card is not Ace as we want cure (51-3) - 48 to Choose second choices there Ceaord Cure poS ible wys hence there are CLi caselii) Spude but not Ace choiceor first Curl irst Care henie there CIre and at seconel Card Ace want no we are (S1-4 = 47 Choicefor there honce Second Card thus 47 12 s in this Ceue there aye pos sible Cime thu urcds total uocu to choose tuo um ber fist Carro s sparde and secondl curel s not Ace So thact are 48 472 48 564 = 612

Answer 2

ANSWER :

N(First card spade excluding spade ace) = 12 

N(First card spade ace) = 1

N(Second card not ace | First card spade excluding spade ace) = 51 - 4 = 47

N(Second not ace | First card is spade ace) = 51 - 3 = 48 

So, N(First card spade and second card not ace)

= N(First card spade excluding spade ace) * N(Second card not ace | First card spade excluding spade ace)

+ N(First card spade ace) * N(Second not ace | First card is spade ace)

= 12 * 47 + 1 * 48 

= 612 (ANSWER).