3 numbers assigned to Men are all greater than that of women. So out of 1 to 6:

The 3 Men can take the following 3 numbers
M - 4,5,6 and women would be W - 1,2,3

So probability of getting 4,5 and 6 = 1/3*1/2*1=1/6 = A.)

-Deepak

DeepakR wrote:3 numbers assigned to Men are all greater than that of women. So out of 1 to 6:

The 3 Men can take the following 3 numbers
M - 4,5,6 and women would be W - 1,2,3

So probability of getting 4,5 and 6 = 1/3*1/2*1=1/6 = A.)

-Deepak

Take another shot Deepak.

1. The men take spots 1,2,3 and the women take spots 4,5,6.

2.The number of ways of organizing the men in a group of 3 is 6, and same with women is 6.

3. So, the total number of ways of organizing the men and women using multiplication rule is 6*6=36.

4. The total number of ways to organize 6 people is 6*5*4*3*2*1=720.

5. So 36/720=1/20

artistocrat wrote:1. The men take spots 1,2,3 and the women take spots 4,5,6.

2.The number of ways of organizing the men in a group of 3 is 6, and same with women is 6.

3. So, the total number of ways of organizing the men and women using multiplication rule is 6*6=36.

4. The total number of ways to organize 6 people is 6*5*4*3*2*1=720.

5. So 36/720=1/20

Good Work Aris! You solved it as in the OA.

Alternatively let 456 be 3 red balls and the rest three black balls

First red 3/6

second red 2/5
3rd red 1/4

Prob men pick all red balls on three random draws is 3/6 x 2/5 x 1/4=1/20