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A person has 2 parents, 4 grandparent...

A person has 2 parents, 4 grandparents, 8 great grandparents, and so on. Find the number of his ancestors during the ten generations preceding his own.

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A person has 2 parents, 4 grandparents, 8 great grand parents, and so on. Find the number of his ancestors during the ten generations preceding his one.

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Pankaj distributes 4 sweets to each student in his class and has 7 sweets left over. Find a rule for the number of sweets he had in terms of the number of students in his class.

The lock of a safe has a dial with holes, sasy ten, in which the numbers 0,1,2,……..9 are inscribed in each hole. The lock can be opened only when a specific code numbersay of six digits is dialled. Suppose the code number is 249916, it means that the can be opened when we first dial 2, then 4 nd so on. Find the maximum number of trials which do not result in opening the lock.

In a certain an algebraical exercise book there and 4 examples on arithmetical progression, 5 examples on permutation and combination, and 6 examples on binomial theorem. Find the number of ways a teacher can select or his pupils at least one but not more than 2 examples from each of these sets.

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A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in the party, is : 469 (2) 484 (3) 485 (4) 468