Q. There are six movie parts numbered from 1 to 6. Find the number of ways in which they be arranged so that part-1 and part-3 are never together.

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Q. 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?

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Q. Find the number of factors of the product 5⁸ * 7⁵ * 2³ which are perfect squares.

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Q. From a group of 8 men and 6 women, five persons are to be selected to form a committee so that at least 3 women are there on the committee. In how many ways can it be done?

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Q. Calculate sum of divisors of n = 1900.

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Q. Given the factorization of a number n, then the sum of divisors can be computed in _______

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Q. Calculate the sum of divisors of N = 9600.

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Q. Find the number of odd positive integers of the number 456.

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Q. The number of even positive integers of 3200 is _______

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Q. What is the sum of divisors of the number 1872?

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Q. Find the odd positive integer of the number 6500.

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Q. How many even positive integers are there in the number 7362?

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Q. Calculate sum of divisors of n = 8620.

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Q. Find the odd positive integer of the number 4380.

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Q. For a gaming competition, 8 girls are planning on splitting up into 3 (non-empty) groups. How many ways can they split up into these groups?

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Q. In a picnic with 20 persons where 6 chocolates will be given to the top 8 children(the chocolates are distinct: first, second). How many ways can this be done?

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Q. How many ways can one choose 20 cookies from 45 different types (assuming there are at least 20 of each type)?

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Q. Assume that it is an afternoon. What is the time on the 24 hour clock after 146 hours?

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Q. There are 28 identical oranges that are to be distributed among 8 distinct girls. How many ways are there to distribute the oranges?

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Q. There are 5 distinct fruits. How many ways can they be planted into identical fruit plants?

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