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From a deck of 52 playing cards, 5 cards are to be drawn.
1. How many set of 5 cards are possible if there are 2 aces and 3 jacks?
2. How many set of 5 cards are possible if all cards are black?
3. How many set of 5 cards are possible if all cards are diamonds?
4. How many set of 5 cards are possible if there are 3 face-cards, 1 king, and 1 spade?
From a deck of 52 playing cards, 5 cards are to be drawn.
1. How many set of 5 cards are possible if there are 2 aces and 3 jacks?
2. How many set of 5 cards are possible if all cards are black?
3. How many set of 5 cards are possible if all cards are diamonds?
4. How many set of 5 cards are possible if there are 3 face-cards, 1 king, and 1 spade?
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Answer:
If your topix is about permutation and combination this would probably the answer.
1. Number of possible 3-jacks combinations = 4. Number of possible 2-aces combinations = 4!/2!2! = 6.
4!/2!2!
=4 × 3 × 2 × 1 / 2 × 1 × 2 × 1
=24
The answer is the product, which is 24.
2. 5!
5!
= 5 × 4 × 3 × 2 × 1
= 2598960 different ways to choose 5 cards from the available 52 cards.
3.
13C3 * 39C2 = 286 * 741 = 211,926 hands contain exactly three diamonds.
13C4 * 39C1 = 715 * 39 = 27,885 hands contain exactly four diamonds.
13C5 * 39C0 = 1287 hands contain five diamonds.
211,926 + 27,885 + 1,287 = 241,098
4. This can be shown in two cases:
Case 1: If king is not drawn,we have
(8/3) × (4/1) × (4/1) = 896 ways
Case 2: If king is drawn,
(4/3) × (3/1) × (4/1) =48 ways
The total number of ways is
896 + 48= 944 ways.
Correct me if I'm wrong
Hope this helps you
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