statistics

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1. This problem is the same as putting 6 items in 4 bins.
Different ways of solving this problem would be:
1. enumerate in a systematic way:
0006
0015
0024
0033
...
6000
and count how many you've come up with.
Note that since the children are of different ages, and the gifts are distinct, 0006 is not the same case as, for example, 0600.

2. the number of ways of distributing n objects into k bins can be modelled by expanding the expression (a+b+c...+k)^n. The number of terms of the expansion represents the number of ways required.
For 6 gifts for 4 children, you would expand (a+b+c+d)^6 and count the number of terms (86) after expansion.

(3) read up on "partitions" and "generating functions" (which is probably part of your course curriculum). You should find much information in books on combinatorics, for example your textbook. If you need recommendations, please post.

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posted by MathMate
2. Sorry, I had a miscount.
The number of terms of the expansion of (a+b+c+d)^6 is 84 (not 86).

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posted by MathMate

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