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For Students who are passionate for Mathematics and want to pursue it for higher studies in India and abroad.

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Try this problem from ISI MStat 2018 PSA Problem 14 based on all possible colorings. We provide sequential hints to help you solve the problem.

A flag is to be designed with 5 vertical stripes using some or all of the four colours: green, maroon, red and yellow. In how many ways can this be done so that no two adjacent stripes have the same colour?

- 576
- 120
- 324
- 432

Basic counting principles

But try the problem first...

Answer: is 324

Source

Suggested Reading

ISI MStat 2018 PSA Problem 14

A First Course in Probability by Sheldon Ross

First hint

How many ways you can colour the first stripe and the second stripe?

You have 4 colour options for the first stripe.

You have (4-1) = 3 colour options for the second stripe.

\( 4 \times 3 \).

Second Hint

How many ways you can colour the third stripe and the rest of the stripes?

You have (4-1) = 3 colour options for the second stripe.

You have (4-1) = 3 colour options for the fourth stripe.

You have (4-1) = 3 colour options for the fifth stripe.

Final Step

Therefore, total number of ways to colour = \( (4 \times 3) \times 3 \times 3 \times 3 = 324 ) \)

What to do to shape your Career in Mathematics after 12th?

From the video below, let's learn from Dr. Ashani Dasgupta (a Ph.D. in Mathematics from the University of Milwaukee-Wisconsin and Founder-Faculty of Cheenta) how you can shape your career in Mathematics and pursue it after 12th in India and Abroad. These are some of the key questions that we are discussing here:

- What are some of the best colleges for Mathematics that you can aim to apply for after high school?
- How can you strategically opt for less known colleges and prepare yourself for the best universities in India or Abroad for your Masters or Ph.D. Programs?
- What are the best universities for MS, MMath, and Ph.D. Programs in India?
- What topics in Mathematics are really needed to crack some great Masters or Ph.D. level entrances?
- How can you pursue a Ph.D. in Mathematics outside India?
- What are the 5 ways Cheenta can help you to pursue Higher Mathematics in India and abroad?

Cheenta has taken an initiative of helping College and High School Passout Students with its "Open Seminars" and "Open for all Math Camps". These events are extremely useful for students who are really passionate for Mathematic and want to pursue their career in it.

Cheenta is a knowledge partner of Aditya Birla Education Academy

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.

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