Anonymous
Anonymous asked in Games & RecreationCard Games · 5 months ago

A 6 card hand is dealt. How many hands have 3 kings and the ace of spades?

2 Answers

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  • 5 months ago

    The probability would be...

    = (1/52)(4/51)(3/50)(2/49)(48/48)(47/47)

    = (1/52)(4/51)(3/50)(2/49)(1)(1)

    = (1*4*3*2)/(52*51*50*49)

    = (1*1*3*2)/(13*51*50*49)

    = (1*1*3*1)/(13*51*25*49)

    = (1*1*1*1)/(13*17*25*49)

    = 1 / (13*17*25*49)

    = 1 / 270,725 or ~0.000369% of this happening.

    For the number of possible hands, we must look at ONLY the numerators.  So it would be...

    = 1 * 4 * 3 * 2 * 48 * 47

    = 24 * 48 * 47

    = 54,144 possible permutations...  HOWEVER if we don't care about order, we must halve this amount to eliminate redundancies, so it give you 26,072 combinations with a 6-card hand.

  • 5 months ago

    Most likely zero.  But I suppose it could be 1.

    Can't be more, you only said "a" hand is dealt.

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