Most of you have learned ‘Set Theory’, and ‘Permutation & Combination’ in your academic life. But the interesting thing is, after passing the exam, many of you have forgotten it because you didn’t enjoy it. Some of you can still remember those formulas, and principles. Again, the interesting thing is, most of you didn’t discover its usefulness in real-life. You learned math, you practiced math, just because you had to. You needed to pass the exam.

Thus math remained a scary and a boring subject to most of you.

Interestingly, math is not a boring subject. It is much tastier than your favorite food. But the thing is, you need to fall in love ❤ with it. If you start loving it, you will have an amazing adventure which will help you to uncover its mystery. Trust me, you will enjoy it then.

The aim of this blog is to give you an idea, how mathematical formulas can be used to solve real-life problems*. Today I will give you a series of interesting problems, which will need mathematical skills from ‘Set Theory’, ‘Permutation’ and ‘Combination’. I hope you will enjoy it.

Observe the below images and then read the following passage.


Suppose your business has two VIP clients – Mr. Mazumdar from ABC Group and Mr. Kanchan from ENA Group. You have invited them to your office for having lunch. From your CRM database, you have come to know the food choice set of both and formed two individual sets, which are as follows –

M (Mr. Mazumdar) = {Steamed rice, Hilsha Fish, Mutton, Beef, Yogurt}

K (Mr. Kanchan) = {Steamed rice, Shrimp, Chicken, Mutton, Yogurt}

Now, you have to calculate the followings –

  1. What will be the total number of items in the lunch menu if you want to satisfy them both? Express in set.
  2. What will be the menu items if you decide not to discriminate anyone by serving different items? Express in set. 
  3. In how many ways the total number of items (found in ‘a’) can be arranged?
  4. Of the total items (found in ‘a’), how many ways can four items be selected provided there must be Streamed rice and Yogurt in the selection?
  5. Suppose after the lunch 5 more persons joined you who are – Mr. & Mrs. Patwary, Mrs. Kanchan, Mrs. Mazumdar, and your wife. In how many ways all of you can sit in a round table so that each man has their own woman adjacent?
  6. If the round table seating arrangement is plotted on a graph paper, it is found – the position of Mrs. Kanchan, Mrs. Patwary and Mrs. Mazumdar are (4,4), (4-4), and (-4,-4) respectively. Prove that – their (three woman’s) seating arrangement formed a right-angled triangle.
  7. In how many ways a committee of two men and two women can be formed from all of you?

I hope you have enjoyed it. If you have any question regarding this problem, feel free to put your comment below. I will respond ASAP.

*P.S. Math always solves real-life problem. You just need to find, how.