JEE Advanced 2026 · Paper 1, Mathematics question 11

Once each person's red count $r_i$ is fixed, the blue counts $6-r_i$ follow. So count solutions of
$$r_1+r_2+r_3+r_4=10,\qquad0\le r_i\le6.$$
(The blue total is then $24-10=14$ automatically.)

• Without the upper bound: $\binom{13}{3}=286$.
• Some $r_i\ge7$ (at most one can be): $4\binom{6}{3}=80$.

Answer $286-80=206$.