A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed, is :
Solution
Given,<br/><br/>Number of Indians = 6<br/><br/>Number of foreigners = 8<br/><br/>Committee of at least 2 Indians and double number of foreigners is to be formed. Hence, the required cases are<br/><br/>(2I, 4F) + (3I, 6F) + (4I, 8F)<br/><br/>= $${}^6{C_2} \times {}^8{C_4} + {}^6{C_3} \times {}^8{C_6} + {}^6{C_4} \times {}^8{C_8}$$<br/><br/>= (15 $\times$ 70) + (20 $\times$ 28) + (15 $\times$ 1)<br/><br/>= 1050 + 560 + 15 = 1625
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
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