Question

Two cards are drawn one after the other from a standard deck of 52 cards.

(a) In how many ways can one draw first a spade and then a heart?
(b) In how many ways can one draw first a spade and then a heart or a diamond?
(c) In how many ways can one draw first a spade and then another spade?

(d) Do the previous answers change if the first card is put back in the deck before the second card is drawn?

Answer 1

Total no of cards=52

we have 13 spades, 13 diamonds, 13 hearts and 13 clubs here.

a) here, one draw first a spade and then a heart.

we can choose a spade among 13 spades that have in wasys i.e. 13 ways

we can choose the next heart among 13 hearts that we have in ways i.e. 13 ways.

So, total no of ways this can be done is= 13*13=169

b)

here, one draw first a spade and then a heart or a diamond.

we can choose a spade among 13 spades that have in wasys i.e. 13 ways

we can choose the next heart or a diamond among (13+13)=26 cards that we have in ways i.e. 26 ways.

So, total no of ways this can be done is= 13*26=338

c)

here, one draw first a spade and then another spade.

we can choose a spade among 13 spades that have in wasys i.e. 13 ways

we can choose the next spade among (13-1)=12 spade that we have in ways i.e. 12 ways.

So, total no of ways this can be done is= 13*12=156

d) if the first card is put back in the deck before the second card is drawn, the 1st two cases (a) and (b) will be unchanged as drawing of second card doesn't depend the 1st card drawn.

but in the third case,

here, one draw first a spade and then put it back and draw another spade.

we can choose a spade among 13 spades that have in wasys i.e. 13 ways. and then we put it back in deck and now the total no of cards is still 13.

we can choose the next spade among 13 spades that we have in ways i.e. 13 ways.

So, total no of ways this can be done is= 13*13=169

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