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Ten points are marked on a straight line and eleven points are marked on another straight line. How many triangles can be constructed with vertices from among the above points?

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We can get the triangles in
two different ways.

Taking two points from the line having 10 points

(in ^{10}_{}2

So,
the number of triangles here is

Taking
two points from the line having 11 points (in ^{11}_{}2

Total number of triangles, =495+550

How many 4 - digit numbers that can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

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How many positive numbers less than 10,000 are such that the product of their digits is 210?

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(Only 2*3 makes the single digit 6).

So, four digit numbers with combinations of the digits {1,6,5,7} and {2,3,5,7} and three digit numbers with combinations of digits {6,5,7} will have the product of their digits equal to 210.

{1,6,5,7} # of combinations 4!=24

{2,3,5,7} # of combinations 4!=24

{6,5,7} # of combinations 3!=6

24+24+6=54.

Let n be the number of different 5 digit numbers, divisible by 4 that can be formed with the digits 1,2, 3, 4, 5 and 6, with no digit being repeated. What is the value of n ?

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Abhijeet Kushwaha

What is the largest number of positive integers to be picked up randomly so that the sum of
difference of any two of the chosen numbers is divisible by 10?

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From a group of 7 men and 6 women, a committee of 5 persons with more males than females is to be formed. In how many ways can this be done?

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