Search any question & find its solution
Question:
Answered & Verified by Expert
The total number of ways of forming a committee of 5 members out of 7 Indians, 6 Americans, 5 Russians and 4 Australians so that every committee contains at least one member from each country is
Options:
Solution:
1247 Upvotes
Verified Answer
The correct answer is:
7560
7I, 6A, 5R, 4AU
$$
\begin{aligned}
& 2 \mathrm{I}+1 \mathrm{~A}+1 \mathrm{R}+1 \mathrm{AU}={ }^7 C_2 \times{ }^6 C_1 \times{ }^5 C_1 \times{ }^4 C_1=2520 \\
& 1 \mathrm{I}+2 \mathrm{~A}+1 \mathrm{R}+1 \mathrm{AU}={ }^7 C_1 \times{ }^6 C_2 \times{ }^5 C_1 \times{ }^4 C_1=2100 \\
& 1 \mathrm{I}+1 \mathrm{~A}+2 \mathrm{R}+1 \mathrm{AU}={ }^7 C_1 \times{ }^6 C_1 \times{ }^5 C_2 \times{ }^4 C_1=1680 \\
& 1 \mathrm{I}+1 \mathrm{~A}+1 \mathrm{R}+2 \mathrm{AU}={ }^7 C_1 \times{ }^6 C_1 \times{ }^5 C_1 \times{ }^4 C_2=1260 \\
& \text { Total }=2520+2100+1680+1260=7560 .
\end{aligned}
$$
$$
\begin{aligned}
& 2 \mathrm{I}+1 \mathrm{~A}+1 \mathrm{R}+1 \mathrm{AU}={ }^7 C_2 \times{ }^6 C_1 \times{ }^5 C_1 \times{ }^4 C_1=2520 \\
& 1 \mathrm{I}+2 \mathrm{~A}+1 \mathrm{R}+1 \mathrm{AU}={ }^7 C_1 \times{ }^6 C_2 \times{ }^5 C_1 \times{ }^4 C_1=2100 \\
& 1 \mathrm{I}+1 \mathrm{~A}+2 \mathrm{R}+1 \mathrm{AU}={ }^7 C_1 \times{ }^6 C_1 \times{ }^5 C_2 \times{ }^4 C_1=1680 \\
& 1 \mathrm{I}+1 \mathrm{~A}+1 \mathrm{R}+2 \mathrm{AU}={ }^7 C_1 \times{ }^6 C_1 \times{ }^5 C_1 \times{ }^4 C_2=1260 \\
& \text { Total }=2520+2100+1680+1260=7560 .
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.