1. **Problem 200:** Find the units digit of $n = 33^{43} + 43^{33}$. 2. **Step 1:** Units digit depends only on the units digit of the base and the exponent. 3. Units digit of 33 is 3, units digit of 43 is 3. 4. We need units digit of $3^{43} + 3^{33}$. 5. Powers of 3 cycle every 4 in units digit: $3^1=3$, $3^2=9$, $3^3=7$, $3^4=1$, then repeats. 6. Find $43 mod 4$: $43 mod 4 = 3$, so units digit of $3^{43}$ is 7. 7. Find $33 mod 4$: $33 mod 4 = 1$, so units digit of $3^{33}$ is 3. 8. Sum units digits: $7 + 3 = 10$, units digit is 0. 9. **Answer for 200:** Units digit is 0 (Option A). 10. **Problem 201:** Team A lines up 3 males and 3 females in order male, female, male, female, male, female. How many different lineups? 11. Positions for males: 3 spots, males can be permuted in $3! = 6$ ways. 12. Positions for females: 3 spots, females can be permuted in $3! = 6$ ways. 13. Total lineups = $6 imes 6 = 36$. 14. **Answer for 201:** 36 (Option D). 15. **Problem 202:** $d = \frac{1}{2^3 \times 5^7}$ expressed as terminating decimal. How many nonzero digits does $d$ have? 16. Simplify denominator: $2^3 \times 5^7 = 2^3 \times 5^3 \times 5^4 = 10^3 \times 5^4$. 17. Rewrite $d = \frac{1}{10^3 \times 5^4} = \frac{1}{10^3} \times \frac{1}{5^4} = 0.001 \times \frac{1}{625}$. 18. $\frac{1}{625} = 0.0016$ (since $625 \times 0.0016 = 1$). 19. So $d = 0.001 \times 0.0016 = 0.0000016$. 20. The decimal is $0.0000016$ which has one nonzero digit (6). 21. **Answer for 202:** One (Option A).