Question

Counting question

Answer 1

\(\large \color{black}{\begin{align}
& \normalsize \text{The number of ways of dividing 10 different balloons }\hspace{.33em}\\~\\
& \normalsize \text{in two groups each containing 5 balloons is ? }\hspace{.33em}\\~\\
\end{align}}\)

Answer 2

I think that the requested number is:
\[\Large 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 = \left( {\begin{array}{*{20}{c}}
{10} \\
5
\end{array}} \right) \cdot 5!\]

Answer 3

but answer given is \(\large \dfrac{10!}{5!5!2!}\)

Answer 4

I'm sorry!

Answer 5

sometimes their is typo in book too

Answer 6

I don't think that it is a typo, I think that my answer is incorrect!

Answer 7

if we have n elements, then for each subset of k elements I have a subset of n-k elements, we have:
\[\Large \left( {\begin{array}{*{20}{c}}
n \\
k
\end{array}} \right) = \left( {\begin{array}{*{20}{c}}
n \\
{n - k}
\end{array}} \right)\]

Answer 8

this applies for n different elements right

Answer 9

yes! In our case we have n=10 and k=5

Answer 10

ohk thanks

Answer 11

I think that the requested number of ways is given by the total number of subset divided by 2=2!

Answer 12

sinceeach way, gives two subsets of 5 elements

Answer 13

since each*

Answer 14

ok