Question

Permutation: how many four letter word can you make out of SUMMER?

Answer 1

numbers of permutations of n elements are:
\[\Large n!\]

Answer 2

would it be 5! * 2?

Answer 3

we have to count how many subset of four elements I can make with 6 elements

Answer 4

How would I do that?

Answer 5

more precisely, we have to count how many subsets of four elements, we can make with 6 elements, being those subset different by the order of their elements or by the type of elements.
In general, if we want to get howm many k elements subsets we can form with n elements, we have to apply this formula:
\[\large {D_{n,k}} = n \cdot \left( {n - 1} \right) \cdot \left( {n - 2} \right) \cdot \left( {n - 3} \right) \cdot ... \cdot \left( {n - k + 1} \right)\]
Now, in your case k=4 and n=6

Answer 6

\[\Large {D_{n,k}}\] isa called the numbers of simple dispositions

Answer 7

so is it 5 P 4 + 6 * 4 P 2?

Answer 8

if we apply my formula above, we get:
\[\Large \begin{gathered}
{D_{n,k}} = n \cdot \left( {n - 1} \right) \cdot \left( {n - 2} \right) \cdot \left( {n - 3} \right) \cdot ... \cdot \left( {n - k + 1} \right) = \hfill \\
= 6 \cdot 5 \cdot 4 \cdot 3 = ...? \hfill \\
\end{gathered} \]

Answer 9

\[\large \begin{gathered}
{D_{n,k}} = n \cdot \left( {n - 1} \right) \cdot \left( {n - 2} \right) \cdot \left( {n - 3} \right) \cdot ... \cdot \left( {n - k + 1} \right) = \hfill \\
= 6 \cdot 5 \cdot 4 \cdot 3 = ...? \hfill \\
\end{gathered} \]

Answer 10

sorry for my first post, I have misunderstood your question!

Answer 11

Ahah no worries :) tyyy