Given: Five cards are drawn from a pack of 52 cards.
By using the formula,
P (E) = \( \dfrac{favourable\; outcomes }{total\; possible\; outcomes}\)
Five cards are drawn at random,
Total possible outcomes are 52C5
n (S) = 2598960
(i) Let E be the event that exactly only one ace is present
n (E) = 4C148C4 = 778320
P (E) =\( \dfrac{ n (E) }{ n (S)}\)
= \(\dfrac{ 778320} { 2598960}\)
= \(\dfrac{ 3243}{10829}\)
(ii) Let E be the event that at least one ace is present
E = {1 or 2 or 3 or 4 ace(s)}
n (E) = 4C148C4+4C248C3+4C348C2+4C448C1 = 886656
P (E) =\( \dfrac{ n (E) }{ n (S)}\)
=\(\dfrac{ 886656 }{ 2598960}\)
= \(\dfrac{ 18472}{54145}\)
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