Matilda has 31 llamas. (a) She first hands out 17 identical llama treats, making
ID: 3013413 • Letter: M
Question
Matilda has 31 llamas.
(a) She first hands out 17 identical llama treats, making sure that no llama receives
more than one treat. In how many ways can she do this?
(b) She then puts 5 distinct decorative collars on llamas, again making sure that no
llama receives more than one collar. In how many ways can she do this? For each
part, show all your work, and briefly JUSTIFY your answer. In particular, you
should not just have numbers; you should give some indication of the method you
are using, and how it applies here.
Explanation / Answer
(a) As llama treats are identical therefore any llama received any llama treats will not make any difference.
Therefore only need to select 17 llama from 31
Therefore no. of ways = 31C17
(b) As collars are distinct
Suppose llama 1 get 1st collar and llama 2 get 2nd collar
and llama 1 get 2nd collar and llama 1 get 1st collar
These will be different cases as collars are distinct.
Therefore We need to arrange 5 out of 31 llama
Therfore no. of ways = 31P5