Arrangements of children by age

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Question from shani, a parent:

How many different arrangements of children by age can there be in families with four children?(hint: Boy-girl-boy-girl is different from boy-girl-girl-boy. Presume there are no twins)
The hint is more confusing than the question. Parent needs to know how to solve this for my own sanity. Mum(karen) needs to help Shani.

Shani and Karen,

What you have to do is write down a sequence of length 4 consisting of B's and G's, for example: BBBB, BGGB, GBGB, etc. There are 2 choices for the first place (B or G) and so on 2 choices for each subsequent place thus you can write down 2x2x2x2 = 16 different sequences.

Penny

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