# 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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- M3Lv 710 years agoFavorite 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

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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

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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 !

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