TCS Company Numerical Ability Probability

7 indians,4americans,2germans are to be seated on 13 chairs for a photograph if a photograph is clicked .what is the probability that in the photo no 2 indians are together
a)7!4!2!/13!
b)7!6!/13!
c)7!/13!
d)7/123

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TCS Other Question

How many positive numbers not greater than 4300 can be formed using the digits 0,1,2,3,4 where repeatation is allowed?

Options: a)576 b)575 c)620 d)640
Unity in Diversity Public school is an elite public school that boasts of having students from various states of India. The school conducts inter class essay writing competition for 10th standard for which exactly six students P, Q, R, S, T, and U compete. The judge of the competition awards exactly four medals, one for each of first, second, third, and fourth (consolation) places, to the top four of the participants. The information that follows is all that is available about the six participants:

-Each participant is either a Keralite or a Gujarati, but not both.
-Two of the six participants are female and four are male.
-The judge awards medals to both female participants, exactly one of which is a Gujarati.
-Exactly one Gujarati wins a medal.
-Participants P and R place ahead of participant S, and participant S places ahead of participants Q and T.
-Participants P and R are Keralites.
-Participants S and U are Gujaratis.
then Which one of the following statements CANNOT be true?

a)A female Keralite wins the second place medal.
b)A female Gujarati wins the second place medal.
c)A male Keralite wins the fourth place medal.
d) A female Gujarati wins the third place medal.