Ask Question
8 April, 09:29

SHOW WORK

If a person can select 7 cups from 10 cups at a coffee shop, how many different combinations are there?

+3
Answers (1)
  1. 8 April, 11:52
    0
    There are 604800 ways of selecting 7 cups from 10 cups.

    Solution:

    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 number of selecting 7 cups from 10 cups = 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.
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “SHOW WORK If a person can select 7 cups from 10 cups at a coffee shop, how many different combinations are there? ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers