Question

Consider a regular deck of 52 cards with 4 suits (diamonds, hearts, clubs, and spades) of 13 cards each

(valued 1, 2, . . . , 10, J, Q, K).

What is the probability of drawing 4 consecutive diamonds? (also consecutive in number)

Answer 1

4 consecutive diamonds probability :

P(4 diamonds) = (select 4 diamond cards from 13 diamond cards)/(select 4 diamond cards from 52 cards)

= (13C4) / (52C4)

= (13*12*11*10)/(52*51*50*49)

= 0.002641

for it to be in consecutive numbers

we divide it by number of arrangements of 4 selected cards as only one of the arrangements of 4 cards will be such that the 4 are consecutive inn number

P(4 consecutive numbered diamonds) = P(4 diamonds) / 4!

= 0.002641 / (4*3*2*1)

= 0.00011

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