IIT JEE , AIEEE Forum - Mathematics , Algebra

peter_pete

Q-out of 100 numbers 6 numbers are selected and put in a line what is the probability that the rectangular tiles whose dimension are first three numbers can be put into boxes whose dimension is equal to the last three numbers.

(THIS PROBLEM WAS given IN DISCUSS WITH COMMUNITY BUT NOBODY COULD SOLVE IT.)

cvramana

The question is not clear.

Once it is mentioned numbers, then next tiles and then boxes!

Can any body tell what is the relation between these things?

titun

The problem is very clear. I will first try to explain it & then give the solution.

6 nos are chosen from first consecutive 100 natural nos.

The first 3 of the chosen nos give the dimensions of the tiles(i.e its length, breadth & height). The last 3 chosen nos give the length, breadth & height of the rectangular box.

The tile will go into the box if the product of the first 3 nos (i.e the vol. of the tile) is less than the product of the last 3 nos (i.e. the vol. of the box)

There can be 3 cases:

1. The product of the first 3 nos i.e the vol of the tile < the product of the last 3 nos i.e. the vol of the box.

2. The product of the first 3 nos i.e the vol of the tile > the product of the last 3 nos i.e. the vol of the box.

3. The product of the first 3 nos i.e the vol of the tile = the product of the last 3 nos i.e. the vol of the box.

Hence, the reqd probability = 1/3

PLZ TELL ME IF I AM WRONG ANYWHERE

cvramana

Thank You titun. You have explained the problem very very clearly. And I feel that the answer is correct. Thank you once again.

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