1. 2/3 of the committee members are men.
2. 3/8 of the men are Americans.
3. 3/5 of the committee members are French.

From the first point, if 2/3 of the members are men, then 1/3 must be women.

Now, let's find out what fraction of the committee members are American men:

• Out of the 2/3 of the members who are men, 3/8 are American. So, the fraction of American men is 2/3​×3/8​=1/4.

Now, let's find out what fraction of the committee members are French men:

• Since 3/5 of the committee members are French and 2/3 of them are men, the fraction of French men is 3/5​×2/3​=2/

Now, let's find out the fraction of American women:

• We know that 1/3 of the committee members are women. Out of these women, the fraction who are American is the remaining fraction after we subtract the fraction of American men (1/4) and French men (2/5) from 1/3.

1/3−1/4−2/5=20/60​−15/60​−24​/60=21/60​

So, the fraction of American women is 21/60​= 7/20​.