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Mathematics: Post your doubts here!

H

hassam

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DragonCub said:
The (i) part is always the most direct in all P & C questions :D
14P12 = 4.36E^10
(ii) -The 3 seats on the right are taken by the 3 businessmen. So first it's 3P3.
-Then the Lins sit in a row on the same side of the aisle, the available locations could only be the 3 pairs of seats on the upper part. (Front pair excluded since taken byy the businessmen.) Moreover the couple can switch seats with each other. It's 3P1 × 2P2.
-Next are the Browns. 1 pair in the 3 taken by the Lins, so for them, 2P1 × 2P2.
-Finally, the students. You can see there are just the right number of seats left: 5 window seats for 5 students. 5P5.
Answer: 3P3 × 3P1 × 2P2 × 2P1 × 2P2 × 5P5 = 17280
(iii) If they seat randomly, we are back to (i) then. Total number of arrangements is 4.36E^10
-If to ensure that Mrs Brown in the front, there are only 3 seats for her to sit in. 3P1
-To ensure Mrs Lin behind a student, group her and one student together as a unit. (Note that she cannot switch the seats with that student since she must be behind the student.) For this "unit", there are 10 pairs of seats valid. 10P1.
--There a 5 students that can be grouped with Mrs Lin, so for the case above, it's 5 × 10P1.
-Finally the others. There are 14 - 1 -2 = 11 seats for 12 - 1 - 2 = 9 people. 11P9.
Number of arrangements = 3P1 × 5 × 10P1 × 11P9 =2.99E^9
Probability = 2.99E^9 / 4.36E^10 = 25/364 OR 0.0687

I'm not sure if my answers are correct. :p
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THANXX A MIllion tyms.........solved it 10 times........bt neva complete;y undrstoood thats y did mistake every time......absolutely loved that words............"To ensure Mrs Lin behind a student, group her and one student together as a unit. (Note that she cannot switch the seats with that student since she must be behind the student.) For this "unit", there are 10 pairs of seats valid. 10P1"
 
alphabravocharlie

alphabravocharlie

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asexamskillme111 said:
Yea it is 5040. I got the same when I did 7*6*(6!/3!). What I wanna do is total no of arrangements - arrangements when none of the G's are next to each other.
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You forget one thing, No. of arrangements - No. of arrangements when no G's are next to each other - No. of arrangements when all the G's are together
 
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