<u>Answer</u>:
There are 604800 ways of selecting 7 cups from 10 cups.
<u>Solution:
</u>
Let's for sake of understanding, we simplify our question.
Let's say there are 3 cups A, B, C . In how many ways two cups can be selected.
So for selecting first cup we have three option that are A, B or C.
And once first cup is selected, number of options for selecting second cup is two.
So it is found that number of selecting 2 cups from 3 cups is product of option available for selecting first cup multiplied by option available for selecting second cup = 3 x 2 = 6
So now applying same logic for selecting 7 cups from 10 cups we get
For selecting first cup option available = 10 cups
Once first cup is selected option available to select second cup = 9 cups
Once second cup is also selected option available to select third cup = 8 cups
Once third cup is also selected option available to select fourth cup = 7 cups
Once fourth cup is also selected option available to select fifth cup = 6 cups
Once fifth cup is also selected option available to select sixth cup = 5 cups
Once sixth cup is also selected option available to select seventh cup = 4 cups
So<em> number of selecting 7 cups from 10 cups </em>= 10 x 9 x 8 x 7 x 6 x 5 x 4 = 604800.
Hence there are 604800 ways of selecting 7 cups from 10 cups.
