How many ways are there to divide 4 Indian countries and 4 China countries into 4 groups of 2 each such that at least one group must have only Indian countries?(a) 6(b) 45(c) 12(d) 76This question was posed to me in class test.This key question is from Counting in portion Counting of Discrete Mathematics

How many ways are there to divide 4 Indian countries and 4 China count

1.	How many ways are there to divide 4 Indian countries and 4 China countries into 4 groups of 2 each such that at least one group must have only Indian countries?(a) 6(b) 45(c) 12(d) 76This question was posed to me in class test.This key question is from Counting in portion Counting of Discrete Mathematics
Answer» RIGHT option is (a) 6 Explanation: The number of ways to divide 4+4=8 countries into 4 groups of 2 each is as follows: (^10C2 * ^10C2* ^10C2 * ^10C2)/4! = 30. Since it is required that at least one group must have only Indian countries, we need to subtract 30 from the number of possible groupings where all 4 groups have 1 Indian COUNTRY and 1 CHINA country each. This is equivalent to the number of ways to match each of the 4 Indian countries with one China country: 4! = 24. Therefore, the answer is 30 – 24 = 6.

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