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There are 3 Indians and 3 Chinese in a group of 6 people. How many subgroups of this group can we choose so that every subgroup has at least one Indian?

There are 3 Indians and 3 Chinese in a group of 6 people. How many subgroups of this group can we choose so that every subgroup has at least one Indian? Correct Answer 56 

Case 1 ( 1 Indian)

The possible subgroups can be

1 Indian with 0 Chinese

1 Indian with 1 Chinese

1 Indian with 2 Chinese

1 Indian with 3 Chinese

Sum of case 1 Possible cases :

Case 2 ( 2 Indians)

The possible subgroups can be

2 Indian with 0 Chinese

2 Indian with 1 Chinese

2 Indian with 2 Chinese

2 Indian with 3 Chinese

Sum of case 2 Possible cases :

Case 3 ( 3 Indians)

The possible subgroups can be

3 Indian with 0 Chinese

3 Indian with 1 Chinese

3 Indian with 2 Chinese

3 Indian with 3 Chinese

Sum of case 2 Possible cases :

Total cases :

24 + 24 + 8 = 56

Related Questions

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Read the passage carefully and choose the best answer to each question out of the four alternatives.
Doing an internship at the University of Lille in France, I almost always found myself stuck whenever I had to speak to non-Indians about India or on anything'Indian'. This was more because of the subtle differences in the way the French understood India in comparison to what I thought was 'Indian'. For instance, when I,or any Indian for that matter, say 'Hindi' is an Indian language, what it means is that it is one of the languages widely spoken in India. This need not be similar tothe understanding that the French would have when they hear of 'Hindi' as an Indian language. Because for them Hindi then becomes the only language spoken inIndia. This is a natural inference that the French, Germans, Italians and many other European nationals would tend to make, because that is generally how it is intheir own respective countries. The risk of such inappropriate generalisations made about 'Indian' is not restricted to language alone but also for India's landscape,cuisine, movies, music, climate, economic development and even political ideologies. The magnitude of diversity of one European country can be easily compared tothat of one of the Indian State, isn't it? Can they imagine that India is one country whose diversity can be equated to that of the entire European continent? Theonus is upon us to go ahead and clarify the nuances in 'Indianness' while we converse. But why should one do so? How does it even matter to clarify? What wrong with respect to India are the Europeans responsible for?
Read the passage carefully and choose the best answer to each question out of the four alternatives.
Doing an internship at the University of Lille in France, I almost always found myself stuck whenever I had to speak to non-Indians about India or on anything'Indian'. This was more because of the subtle differences in the way the French understood India in comparison to what I thought was 'Indian'. For instance, when I,or any Indian for that matter, say 'Hindi' is an Indian language, what it means is that it is one of the languages widely spoken in India. This need not be similar tothe understanding that the French would have when they hear of 'Hindi' as an Indian language. Because for them Hindi then becomes the only language spoken inIndia. This is a natural inference that the French, Germans, Italians and many other European nationals would tend to make, because that is generally how it is intheir own respective countries. The risk of such inappropriate generalisations made about 'Indian' is not restricted to language alone but also for India's landscape,cuisine, movies, music, climate, economic development and even political ideologies. The magnitude of diversity of one European country can be easily compared tothat of one of the Indian State, isn't it? Can they imagine that India is one country whose diversity can be equated to that of the entire European continent? Theonus is upon us to go ahead and clarify the nuances in 'Indianness' while we converse. But why should one do so? How does it even matter to clarify? According to the writer the responsibility of explaining the facts about India to Europeans rests with?
Read the passage carefully and select the best answer to each question out of the given four alternatives.
Public opinion may be passive and false or active and real. It is claimed in theory that all governments are ultimately based on the opinion or sanction of the governed. But we find that in practice the people's rights are often trodden down and tyranny and oppression are allowed to continue. The government does it not because the people want it to do so but because they are too idle, too uneducated and too disunited or timid to oppose the govern ment. Such public opinion is passive and false and not an active verdict. But when we find people alert, intelligent and determined to let the government know their will, when they want to exercise actively their voice in the management of their country, we have an instance of true or active public opinion. True public opinion is formed by and expressed through the press, the platform, political parties and educational institutions. These have sacred duties to perform, duties on which depends the ultimate good of the entire community. The press today wields a tremendous influence, So it should support the causes and move ments and condemn the wrong one's and thus teach people to form correct opinion. A free and fair press ventilates the grievances of the public. Thus a healthy relationship develops between the people and the government through out an unbiased press. Political parties also help to create and regulate opinions. No less important part is played by the educational Institutions which train the minds of the young people who will be the citizens of tomorrow. It has been said that modern Germany and China have been made by their universities. It is necessary that the young and the growing minds should imbibe the spirit of fellow-feeling, the spirit of tolerance, the habit of compromise, and show due regard for the feelings and opinion of others without which a democratic society cannot function, let alone succeed. When there is true awakening of the people, we shall have the real and conscious public opinion. And justice will reign on earth and truly will the voice of the people be the voice of God.
What is important for the democratic society to function properly?
Read the passage carefully and select the best answer to each question out of the given four alternatives.
Public opinion may be passive and false or active and real. It is claimed in theory that all governments are ultimately based on the opinion or sanction of the governed. But we find that in practice the people's rights are often trodden down and tyranny and oppression are allowed to continue. The government does it not because the people want it to do so but because they are too idle, too uneducated and too disunited or timid to oppose the govern ment. Such public opinion is passive and false and not an active verdict. But when we find people alert, intelligent and determined to let the government know their will, when they want to exercise actively their voice in the management of their country, we have an instance of true or active public opinion. True public opinion is formed by and expressed through the press, the platform, political parties and educational institutions. These have sacred duties to perform, duties on which depends the ultimate good of the entire community. The press today wields a tremendous influence, So it should support the causes and move ments and condemn the wrong one's and thus teach people to form correct opinion. A free and fair press ventilates the grievances of the public. Thus a healthy relationship develops between the people and the government through out an unbiased press. Political parties also help to create and regulate opinions. No less important part is played by the educational Institutions which train the minds of the young people who will be the citizens of tomorrow. It has been said that modern Germany and China have been made by their universities. It is necessary that the young and the growing minds should imbibe the spirit of fellow-feeling, the spirit of tolerance, the habit of compromise, and show due regard for the feelings and opinion of others without which a democratic society cannot function, let alone succeed. When there is true awakening of the people, we shall have the real and conscious public opinion. And justice will reign on earth and truly will the voice of the people be the voice of God.
Which of the following is not the reason for the oppression caused to general public by the running government in the country?