Question

Number of ways of forming a committee of $6$ members out of $5$ Indians, $5$ Americans and $5$ Australians such that there will be atleast one member from each country in the committee is

• A. 3375
• B. 4375
• C. 3875
• D. 4250

Answer 1

Answer: (B)

4375

Answer 2

Required cases are as follow: $\therefore$ Required number of committee $={ }^{5} C_{1} \times{ }^{5} C_{1} \times{ }^{5} C_{4}+{ }^{5} C_{1} \times{ }^{5} C_{2} \times{ }^{5} C_{3}+{ }^{5} C_{1} \times{ }^{5} C_{3}$ $\times{ }^{5} C_{2}$ $+{ }^{5} C_{1} \times{ }^{5} C_{4} \times{ }^{5} C_{1}+{ }^{5} C_{2} \times{ }^{5} C_{1} \times{ }^{5} C_{3}+{ }^{5} C_{2} \times{ }^{5} C_{2}$ $\times{ }^{5} C_{2}+{ }^{5} C_{2} \times{ }^{5} C_{3} \times{ }^{5} C_{1}+{ }^{5} C_{3} \times{ }^{5} C_{1} \times{ }^{5} C_{2}+{ }^{5} C_{3}$ $\times{ }^{5} C_{2} \times{ }^{5} C_{1}+{ }^{5} C_{4} \times{ }^{5} C_{1} \times{ }^{5} C_{1}$ $= 5 \times 5 \times 5+5 \times 10 \times 10+5 \times 10 \times 10+5 \times 5 \times 5$ $+10 \times 5 \times 10+10 \times 10 \times 10+10 \times 10 \times 5+10 \times 5$ $\times 10+10 \times 10 \times 5+5 \times 5 \times 5$ $= 125+500+500+125+500+1000+500+500$ $+500+125$ $= 4375$