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Number of natural numbers not exceeding 4321 can be formed with the digits 1,2,3,4 if repetition is allowed is

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Important Questions on Permutations & Combinations

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In how many ways can 5 prizes be given away to 4 boys when each boy is eligible for any number of prizes? 
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In how many ways can n balls be randomly distributed in n cells?
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In how many ways can 6 boys form a ring?
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In how many ways can 6 boys be arranged at a round table so that 2 particular boys may be together?
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In how many ways can 6 beads be strung into a necklace?
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In how many ways can 5 men and 2 ladies be arranged at a round table if two ladies are never together?
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9 persons were invited for a business meeting by Ambani, where the host be seated at a circular table. How many different arrangements are possible if two invitees viz., Sahara and Mahindra be seated on either side of the host Ambani?
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There are 3 boys and 4 girls, seated around a circular table so that no two boys are together. Find the number of ways in which this can be done.