Question

Determine the number of 5 cards combination out of a deck of 52 cards if at least 3 out of 5 cards are ace card​

Answer 1

Answer:

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Answer 2

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Explanation:

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• There are total 52 cards in a deck.
• Out of which 26 cards are red and 26 cards are black.
• Out of 26 for both red and black cards 6 are face cards.
• There are total 4 ace in one deck of cards

So, Remaining cards left =52-4=48 cards

Now,come to the question:-

Total Number of ways of selecting =$4C_{3}\times48C_{2}+4C_{4}\times48C_{1}$

$= > {\cancel{4 }}\times \frac{48 \times 47}{\cancel{{2} }} + 1 \times 48$

$= > 2 \times( 48 \times 47 )+ 1 \times 48$

Taking 48 common from both term:-

$= > 48(2 \times 47 + 1)$

$= > 48 ( 94 + 1)$

$= > 48 \times 95$

$= 4560$

Thus,There are 4560 ways to select