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1) In how many ways can 10 pencils (identical) be distributed among 5 children if a) there are no restrictions? b) each child gets at least 1 pencil? c) the oldest child gets at least 2 pencils?

2) How many arrangements of the letters in MISSISSIPPI have no consecutive S' s?

3) In how many ways can a gambler draw 5 cards from a standard deck and get a) a flush (five cards of the same suit) ? b) four aces? c) four of a kind? d) three aces and two jacks e) three aces and a pair? f) a full house (three of a kind and a pair) ? g) three of a kind? h) two pairs?

Please help me to understand this topic because I am very new at this. If you solve them please explain them in some detail or steps. Thanks in advance.

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    @Kannappan: Your link has been Google-mangled. The full set of notes in updated form is at the link *Course Notes* [here](http://www.math.dartmouth.edu/archive/m28w02/public_html/).2012-02-21
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    @Brian Thanks for posting. I have deleted my previous comment.2012-02-22

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