Given: The face cards are removed from a full pack of 52.

By using the formula,

P (E) = \( \dfrac{favourable\; outcomes }{total\; possible\; outcomes}\)

Four cards are drawn from the remaining 40 cards, so we have to find the probability that all of them belong to different suit.

Total possible outcomes of drawing four cards are ^{40}C_{4}

n (S) = ^{40}C_{4} = 91390

Let E be the event that 4 cards belong to different suit.

n (E) = ^{10}C_{1}^{10}C_{1}^{10}C_{1}^{10}C_{1 }= 10000

P (E) =\( \dfrac{ n (E) }{ n (S)}\)

= \(\dfrac{ 10000 }{ 91390}\)

= \( \dfrac{ 1000 }{ 9139}\)

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