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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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This is a beautiful problem from ISI MSTAT 2019 PSA problem 6 based on basic counting principles. We provide sequential hints so that you can try.

How many times does the digit ‘2’ appear in the set of integers \( \{1,2,…,1000\} \)?

- 590
- 600
- 300
- 299

Basic counting principles

But try the problem first...

Answer: is 300

Source

Suggested Reading

ISI MStat 2019 PSA Problem 6

A First Course in Probability by Sheldon Ross

First hint

Let’s count the number of times 2 occurs once.

_ _ _

The position of 2 can be selected in 3 ways. The rest in 9 x 9.

Total number of 2 = **1 **x 3 x 9 x 9 = 243

Second Hint

Let’s count the number of times 2 occurs twice.

_ _ _

The positions of 2 can be selected in 3 ways. The rest in 9.

Total number of 2 = **2 **x 3 x 9 = 54

Final Step

Let’s count the number of times 2 occurs thrice.

The positions of 2 can be selected in 1 way. The rest in 1.

Total number of 2 = **3** x 1 x 1 = 3

Total Number of Such Numbers = 243 + 54 + 3 = 300

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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