Four cards are drawn from a well shuffled pack of 52 cards. Find the probability that it
contains
a) all aces (2)
b) atmost 2 aces. (2)
c) atleast two aces.(2)
Answers
Answer:
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Given : Four cards are drawn from a well shuffled pack of 52 cards.
To Find: the probability that it contains
a) all aces
b) atmost 2 aces
c) atleast two aces
Solution:
4 cards oy of 52 cards can be selected in ⁵²C₄ ways
= 2,70,725
all aces can be selected in ⁴C₄ = 1 ways
Hence probability of all aces = ⁴C₄ / ⁵²C₄
1/2,70,725
atmost 2 aces
= 0 aces + 1 ace + 2 aces
= ⁴C₀*⁴⁸C₄ + ⁴C₁*⁴⁸C₃ + ⁴C₂*⁴⁸C₂
probability = ( ⁴C₀*⁴⁸C₄ + ⁴C₁*⁴⁸C₃ + ⁴C₂*⁴⁸C₂ ) / ⁵²C₄
atleast two aces.(2)
= 2 aces + 3 aces + 4 aces
= ⁴C₂*⁴⁸C₂ + ⁴C₃*⁴⁸C₁ ⁴C₄*⁴⁸C₀
probability = ( ⁴C₂*⁴⁸C₂ + ⁴C₃*⁴⁸C₁ ⁴C₄*⁴⁸C₀ ) / ⁵²C₄
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