6 identical red marbles and 4 identical white marbles are arranged at

Question

6 identical red marbles and 4 identical white marbles are arranged at random in a row. What is the probability that the 2 marbles in the middle are of the same color?

A. 2/45

B. 1/5

C. 4/15

D. 12/25

E. 7/15

saurabhbajpai · Answer

Should be E in my opinion. ((8!/4!*4!)+(8!/6!*2!))/(10!/4!*6!)=7/15

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Todercap · Answer

1) If the 2 marbles in the middle are RED:
- Total ways to arrange 6 red marbles in 10 slots: 10C6 = 210
- Total ways to arrange the remaining 4 red marbles in the available 8 slots: 8C4=70
 70\210

2) If the 2 marbles in the middle are WHITE:
- Total ways to arrange 4 white marbles in 10 slots: 10C4 = 210
- Total ways to arrange the remaining 2 white marbles in the available 8 slots: 8C2=28
 28\210

= 70\210 + 28\210 (\14) = 7\15.

Answer choice E

Evronredor · Answer

Let's use permutation to solve it.

There are two possibilities - 
1) We have two red marbles in the middle
2) We have two White marbles in the middle

Case 1:

Total arrangements: 10!/6!4!
Desired outcome: 8!/4!4! (Fixing the position of the red marbles in the middle and removing them from the total lot of Red marbles plus reducing the total placements by 2)

=70/210

Case 2:

Total arrangements: 10!/6!4!
Desired outcome: 8!/6!2!

= 28/210

P(two Red marbles in the middle or two White marbles in the middle) = 70/210+28/210 = 98/210 = 7/15

Answer: E

Guntabulla · Answer

Is this method correct?

Lets start with filling up the middle slots first:
i) Both Middle slots are red:
5th slot has a 6/10 chance of being red
6th slot will then have a 5/9 chance of being red
Totally that is a 30/90 chance of both slots being red

ii) Both Middle slots are white
5th slot has a 4/10 chance of being white
6th slot will then have a 3/9 chance of being white
Totally that is a 12/90 chance of both slots being white

Adding them up that is a 42/90 chance of both slots being the same color
42/90=7/15

Answer E

Arjun123321 · Answer

We can just use the basic principle of probability, since they have not given condition about other marbles and its arrangement.

They are only concerned with middle marbles being of equal colour.

So probability for Red will be (6/10)*(5/9)

or

probability for white marbles will be (4/10)*(3/9)

And since we need total probability of either case 1 happening OR the case 2 happening, add the two cases, and you will get 7/15

SR4896 · Answer

Total ways= 10!/(6!*4!)
Case 1: 2 Red balls in the middle
Ways: 81/(4!*4!)
Case 2: 2 White balls in the middle
Ways: 8!/(6!*2!)

Prob = (70+28)/210

bumpbot · Answer

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6 identical red marbles and 4 identical white marbles are arranged at

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