[kevin88]

Five cards are chosen from a standard 52 card deck. How many hands include either an Ace or a Spade.

[creahands]

U have 13 spades and 3 extra aces for a total of 16 cards.

U can make 10 -5 card hands with deck. This will give u a possibility of 10 hands with at lest one spade or and ace

Chuck

[ebaines]

I'm afraid creahands's answer is incorrect. The way to approach this is as follows:

As already pointed out, there are 16 cards that satisfy the condition of being either an ace or a spade. That means there are 52-16 = 36 cards that do not satisfy either condition. Here are two ways to continue:

1. First determine how many hands can be dealt with exactly one spade/ace card and 4 others. This would be C(5,1)x16x36*35*34*33. Then add the number of hands that can have two spade/ace cards and three others, plus the number of hands with three spade/ace and 2 others, plus hands with 4 space/ace and 1 other, plus hands with 5 spade/ace and 0 others.

2. An easier way: determine how many total 5-card hands there are in a 52-card deck, then subtract the number of 5-card hands that consist only of non spade/ace cards:

P(52,5) - P(36,5)

[creahands]

If the question is how many combination can be dealt, then my answer is incorrect.

If, however, the question is how many can dealt from a 52 card deck then answer is correct. U can only get 10 hands out of a 52 card deck.

Chuck

[morgaine300]

If the problem meant for the hand to be sat aside, and then pick another hand from what was left, it would say so. And I've never seen a question wanting to know what it is you were stating.

It wants combinations, i.e. one hand could have a crossover with another hand.

[morgaine300]

Speaking of which, shouldn't that be combinations and not permutations?

[Unknown008]

Isn't the question asking for only one spade or one ace?

So, this comes simply to:

[morgaine300]

I wondered about that too. A little on the interpretive side. It says "an" ace or "a" spade. As though they may mean just one of them.