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 ^{52}C_{5}

n (S) = 2598960

**(i)** Let E be the event that exactly only one ace is present

n (E) = ^{4}C_{1}^{48}C_{4 }= 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) = ^{4}C_{1}^{48}C_{4}+^{4}C_{2}^{48}C_{3}+^{4}C_{3}^{48}C_{2}+^{4}C_{4}^{48}C_{1 }= 886656

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

=\(\dfrac{ 886656 }{ 2598960}\)

= \(\dfrac{ 18472}{54145}\)

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