M4maths Previous Puzzles

16 Feb 2010 King of Probability?

In a pack of playing cards, I have to draw any 6 cards. Probability of getting a set of 4 kings
and any of the 2 cards is?

OPtion

1) 2/52455
2) 6/54145
3) 1/57120
4) 5/57120
5) 1/53040
6) 5/53040
7) 3/54145
8) 5/54120
9) 9/58697
10) 3/51115

Solution

No. of methods for selecting 6 cards out of 52 are 52*51*50*49*48*47/6*5*4*3*2*1
Similarly no. of methods for selecting 2 cards out of 48 after selecting 4 kings are
48*47/2*1
Hence probability is (48*47/2*1)/( 52*51*50*49*48*47/6*5*4*3*2*1)
= 3/54145

Correct Option: 7 Best Solution (9)

Dr.Dipin Singh   15 years AGO

Total ways of drawing 6 cards = 52 C 6
.......
Ways of getting 4 kings and 2 other cards = 4C4 * 48C2

Probability of getting a set of 4 kings and any of the 2 cards = 4C4 * 48C2 /52C6= 3/54145 ... option 7

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HARMEET KAUR   15 years AGO

probability = 4c4*48C2/52C6 = 3/54145 ...option 7

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Dimple   15 years AGO

48c2/52c6=3/54145 so option 7.

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Sukham   15 years AGO

Number of ways of selecting 6 cards from 52 cards = 52C6

Total number of ways of getting 4 kings when 6 cards are drawn = 4C4 × 48C2

Probability = 4C4 × 48C2/52C6= 3/54145
..... so option 7

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Rituraj   15 years AGO

Total favourable conditions/all possible conditions = 48C2/52C6 = 3/54145

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Dr. Divya   15 years AGO

from 52 cards, 6 cards can be chosen in 52Combination6 ways.

n(s) = 52C6 = 52! / 6!*46!

4 kings can b chosen in 4C4 ways

and 2 other can b chosen in 48C2 ways.

so the probability is (4C4 * 48C2)/52C6
---------------- = 360/6497400 = 3/54145.


So the answer is 7.

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Karan   15 years AGO

Probability of getting a set of 4 kings
and any of the 2 cards = 4C4*48C2/52C6= 3/54145

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bhuwan adhikari   15 years AGO

probability= 1x48x47x6x5x4x3x2x1/52x51x50x49x48x47x2x1=3/54145

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Saranjit Singh   15 years AGO

Probability of getting a set of 4 kings
and any of the 2 cards = 4C4*48C2/52C6= 3/54145

Like? Yes (1) | No