at a local cafeteria 10 selections of vegetables are available how many 3 vegetable trays may be made

120

Step-by-step explanation:

This is a combination problem in which order does not matter.

You can choose from 10 vegetables for the first choice.

Then you can choose from 9 vegetables for the second choice.

Finally, you can choose from 8 vegetables for the third choice.

That means the total number of choices is 10 * 9 * 8 if the order mattered.

Since choosing the same three vegetables in any order makes the same choice, you need to divide by the number of ways you can arrange 3 vegetables in a plate.

The number of ways you can arrange 3 vegetables in a plate is 3 * 2 * 1.

The number of combinations is (10 * 9 * 8) / (3 * 2 * 1) = 720/6 = 120