Question

You have 16 different cuts of flowers and plan to use seven of them how many different selections of the seven flowers are possible

Answer 1

We can have 11440 different selections.

SOLUTION:

Given, you have 16 different cuts of flowers  

And you have planned to use seven out of them.  

We have to find how many different selections of the seven flowers are possible.  Now, we have to select 7 items out of 16 available items. So we have to use combinations.

Then, 7 out of 16 combination $\rightarrow^{16} \mathrm{c}_{7} \rightarrow \frac{16 !}{(16-7) ! 7 !}$

$\bold{\text{ Since } ^nC_r=\frac{n !}{(r !(n-r) !)}}$

$\begin{array}{l}{\rightarrow \frac{16 !}{9 ! \times 7 !}} \\\\ {\rightarrow \frac{16 \times 15 \times 14 \times 13 \times 12 \times 11 \times 10 \times 9 !}{9 ! \times 7 !}} \\\\ {\rightarrow \frac{16 \times 15 \times 14 \times 13 \times 12 \times 11 \times 10}{7 \times 6 \times 13 \times 12 \times 11 \times 10}} \\\\ {\rightarrow \frac{57657600}{5040}} \\\\ {\rightarrow 11440}\end{array}$

Hence, we can have 11440 different selections.