If 3 cards are selected at random from the deck of 52 cards then What

Question

If 3 cards are selected at random from the deck of 52 cards then What is the probability of one of the selected cards will be King, one of them will be Queen and one of them will be Jack?

A deck of cards has a total of 52 cards, consisting of 4 suits; (spades(Black), hearts(Red), diamond(Red)s, and clubs(Black)); and 13 cards including 1 king, 1 queen and 1 jack in each suit

A) 96/5525
B) 48/5525
C) 16/5525
D) 8/16575
E) 1/2197

Source : https://www.GMATinsight.com

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ENGRTOMBA2018 · Answer

Let K,Q and J represent King, Queen and Jack respectively.

One possible combination is KQJ and this can be arranged in 3! ways.

Probability of KQJ = (4/52)*(4/51)*(4/50)

Total probability = 3! * (4/52)*(4/51)*(4/50) . No need for final calculation. Reduce this to simpler form and you only have 1 option with 16 in the numerator. C is the correct answer.

Sakshij0694 · Answer

Bunuel  - Why is the answer not A?
I chose 3 cards out of a deck of 52  (52c3)

Next as there 4 Kings, 4 Queens, and 4 Jacks in a deck therefore i chose 1 of each individually 4c1 - 4c1 4c1

And the cards can be pulled in any manner so 3!

Overall when i did the calculation part 4*4*4*6/52c3

The answer comes out to be 96/5525

Where is this going wrong?
 
There is no replacement issue here as well.

GMATinsight · Answer

In your calculation here 4*4*4*6/52c3

Numerator includes arrangement but Denominator includes only selection and no arrangement hence your answer is incorrent

Rule of probability

Either calculate both numerator and denominator by selection or both by arrangement

I hope this helps!!!

anvikshashetty · Answer

Total # of possible outcomes = 52C3
Total # of favourable outcomes = 4C1*4C1*4C1 
Req. probability = 4*4*4*1*2*3/52*51*50 ==> once fully reduced, numerator will be 16 --> sufficient to answer the question.

Answer is C.

US09 · Answer

Total number of outcomes: 52C3.
Desired outcomes: 4C1*4C1*4C1.

Probability = (4C1*4C1*4C1)/(52C3) = 16/5625 = C.

JS1290 · Answer

I got D as an answer. 
Probability of picking one king out of 52 cards: 4/52
Probability of picking one queen out of 52 cards: 4/51
Probability of picking one jack out of 52 cards: 4/50

4/52 * 4/51 * 4/50 = option D.

Could someone please tell me where I made a mistake in my solution? Would greatly appreciate it!

gracie · Answer

1st draw: 12/52
2nd draw: 8/51
3rd draw: 4/50
12/52*8/51*4/50➡16/5525
C

GMATinsight · Answer

Method-1   
Probability of KQJ in this specific order = (4/52)*(4/51)*(4/50)
Probability of KQJ in ALL possible orders = 3!*(4/52)*(4/51)*(4/50)

Method-2   
(4C1*4C1*4C1)/52C3

Method-3   
(4/52)*(4/51)*(4/50)*3!
3! is multiplied to include all possible orders of KQJ

bumpbot · Answer

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If 3 cards are selected at random from the deck of 52 cards then What

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