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Q:

How many black cards are in a deck?

A) 13	B) 26
C) 39	D) 52

Answer & Explanation Answer: B) 26

Explanation:

The total cards in the deck are 52. These 52 cards are divided into 4 suits of 13 cards in each suit. Two Red suits and Two black suits.

Red suits :: Heart suit and Diamond suit = 26

Black suits :: Spade suit and Club suit = 26.

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Filed Under: Arithmetical Reasoning
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Q:

From a deck of 52 cards, a 5 card hand is dealt.How many distinct hands can be formed if there are atleast 2 queens?

A) 103336	B) 120000
C) 108336	D) 108333

Answer & Explanation Answer: C) 108336

Explanation:

The total possible cases would be a 5 card hand with no restrictions : $52 C_{5}$ 5

The unwanted cases are:

no queens(out of 48 non-queens cards we get 5) $48 C_{5}$

only 1 queen(out of 4 queens we get 1,and out of 48 non-queens we get 4) $4 C_{1} * 48 C_{4}$

Therefore, $52 C_{5} - (48 C_{5} + 4 C_{1} * 48 C_{4}) = 108336$

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Filed Under: Permutations and Combinations

Q:

From a deck of 52 cards, a 5 card hand is dealt.How may distinct five card hands are there if the queen of spades and the four of diamonds must be in the hand?

A) 52C5	B) 50C3
C) 52C4	D) 50C4

Answer & Explanation Answer: B) 50C3

Explanation:

If the queen of spades and the four of diamonds must be in hand,we have 50 cards remaining out of which we are choosing 3.

So, 50 $C_{3}$

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Filed Under: Permutations and Combinations

Q:

From a deck of 52 cards, a 7 card hand is dealt.How many distinct hands are there if the hand must contain 2 spades and 3 diamonds ?

A) 7250100	B) 7690030
C) 7250000	D) 3454290

Answer & Explanation Answer: A) 7250100

Explanation:

There are 13 spades,we must include 2: 13 $C_{2}$

There are 13 diamonds,we must include 3: $13 C_{3}$

Since we can't have more than 2 spades and 3 diamonds,the remaining 2 cards must be pulled out from the 26 remaining clubs and hearts : $26 C_{2}$

Therefore, $13 C_{2} * 13 C_{3} * 26 C_{2}$ = 7250100

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Filed Under: Permutations and Combinations

Q:

A standard deck of playing cards has 13 spades. How many ways can these 13 spades be arranged?

A) 13!	B) 13^2
C) 13^13	D) 2!

Answer & Explanation Answer: A) 13!

Explanation:

The solution to this problem involves calculating a factorial. Since we want to know how 13 cards can be arranged, we need to compute the value for 13 factorial.

13! = (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) = 6,227,020,800

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Filed Under: Permutations and Combinations

Q:

Determine the total number of five-card hands that can be drawn from a deck of 52 cards.

A) 2589860	B) 2598970
C) 2598960	D) 2430803

Answer & Explanation Answer: C) 2598960

Explanation:

When a hand of cards is dealt, the order of the cards does not matter. If you are dealt two kings, it does not matter if the two kings came with the first two cards or the last two cards. Thus cards are combinations. There are 52 cards in a deck and we want to know how many different ways we can put them in groups of five at a time when order does not matter. The combination formula is used.

C(52,5) = 2,598,960

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Filed Under: Permutations and Combinations

Q:

One card is drawn from deck of 52 cards, each of the 52 cards being equally likely to be drawn. Find the probability that the ball drawn is red.

A) 1/3	B) 1/2
C) 1/4	D) 1/6

Answer & Explanation Answer: B) 1/2

Explanation:

Total number of elementary events = 52

There are 26 red cards,out of which one red card can be drawn in $26 C_{1}$ ways =26.

So,required probability = 26/52 = 1/2

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Filed Under: Probability

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