How many of these hands contain exactly two aces no king and five spades? Combinations pls help?

We know that there are C52,15 ways to deal a 15 card hand from an ordinary

deck of 52 cards (order does not matter). How many of these hands contain

(exactly) two aces, no king and five spades?

2 Answers

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  • M3
    Lv 7
    9 years ago
    Favorite Answer

    it is taken that # of spades is also exactly 5

    aces: 3 non-spade, 1 spade

    kings: 3 non-spade, 1 spade

    other spades: 11

    the rest : 33

    case 1: ace of spades in the hand

    ---------

    1 more ace from 3, 4 more spades from 11, 9 balance from 33

    3c1*11c4*33c9

    case 2: ace of spades not in hand

    ---------

    2 aces from 3, 5 spades from 11, 8 balance from 33

    3c2*11c5*33c8

    add up to get

    ans: 57 424 869 216

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    p.s:

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    i do hope it's a 15 card hand,

    not a 13 card hand !

    if it's the latter, as i suspect,

    you can easily work it out now !

  • 4 years ago

    I think 24

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