Question

Find the number of ways in which 3 boys and 3 girls (all are of different heights) can be arranged in a line so that boys as well as girls among themselves are in decreasing order of height (from left to right).

Answer 1

Boys $\to B_1,B_2,B_3$

Girls $\to G_1,G_2,G_3$

So the problem reduce to finding the patterns of $3$ boys with in $6$ positions corequivalenty $3$ girls within 6 positions

That's just $6$ chore $3\to {}^6{C}_3=\frac{6!}{3!3!}=20$ ways