if each office can recommend 2 members, one male and one female, the potential members of the committee are 12, 6 males and 6 females. Since each office will be represented by 1 person and the committee must have an equal number of males and females, the committee will be formed by exactly 6 people, 3 males and 3 females.
Now we have to select 3 males in a group of 6 males and 3 females in a group of 6 females. Therefore, we use the combination formula: 6!/(3!*3!) -> number of ways of choosing either 3 males out of 6, or 3 females out of 6; and then this result must be squared, to multiply all the possible combinations of males and females.
Finally, the result is: 400
Now we have to select 3 males in a group of 6 males and 3 females in a group of 6 females. Therefore, we use the combination formula: 6!/(3!*3!) -> number of ways of choosing either 3 males out of 6, or 3 females out of 6; and then this result must be squared, to multiply all the possible combinations of males and females.
Finally, the result is: 400