Cheenta
Academy for Gifted Students
Get inspired by the success stories of our students in IIT JAM MS, ISI  MStat, CMI MSc DS.  Learn More

# ISI MStat 2019 PSA Problem 4 | Basic counting principle

This is a beautiful problem from ISI MSTAT 2019 PSA problem 4 based on basic counting principles. We provide sequential hints so that you can try.

## Basic Counting Principles - ISI MStat 2019 PSA - 4

What is the number of 6 digit positive integers in which the sum of the digits is at least 52?

• 66
• 24
• 28
• 120

### Key Concepts

Basic counting principles

## Check the Answer

Answer: is

ISI MStat 2019 PSA Problem 4

A First Course in Probability by Sheldon Ross

## Try with Hints

Find the Minimum Digit for each case of sum of the digits (S).

S = 54, Minimum Digit = 9

S = 53, Minimum Digit = 8

S = 54, Minimum Digit = 7 or 8

Let's find the Second Minimum Digit and the Third Minimum Digit  for S = 53 and S = 52.

S = 53,
Second Minimum = 9

S = 52,
Minimum Digit = 7,
Second Minimum = 9

S = 52,
Minimum Digit = 8,
Second Minimum = 8,
Third Minimum = 9

Now it's time for counting

S = 54
{999999}

S = 53,
{8,9,9,9,9,9} : Total = 6

S = 54,
{7,9,9,9,9,9} : Total = 6
{8,8,9,9,9,9} : Total = 15

Hence in total there are 1+6+6+15=28 such numbers .

## Subscribe to Cheenta at Youtube

This is a beautiful problem from ISI MSTAT 2019 PSA problem 4 based on basic counting principles. We provide sequential hints so that you can try.

## Basic Counting Principles - ISI MStat 2019 PSA - 4

What is the number of 6 digit positive integers in which the sum of the digits is at least 52?

• 66
• 24
• 28
• 120

### Key Concepts

Basic counting principles

## Check the Answer

Answer: is

ISI MStat 2019 PSA Problem 4

A First Course in Probability by Sheldon Ross

## Try with Hints

Find the Minimum Digit for each case of sum of the digits (S).

S = 54, Minimum Digit = 9

S = 53, Minimum Digit = 8

S = 54, Minimum Digit = 7 or 8

Let's find the Second Minimum Digit and the Third Minimum Digit  for S = 53 and S = 52.

S = 53,
Second Minimum = 9

S = 52,
Minimum Digit = 7,
Second Minimum = 9

S = 52,
Minimum Digit = 8,
Second Minimum = 8,
Third Minimum = 9

Now it's time for counting

S = 54
{999999}

S = 53,
{8,9,9,9,9,9} : Total = 6

S = 54,
{7,9,9,9,9,9} : Total = 6
{8,8,9,9,9,9} : Total = 15

Hence in total there are 1+6+6+15=28 such numbers .

## Subscribe to Cheenta at Youtube

This site uses Akismet to reduce spam. Learn how your comment data is processed.

### Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy

### Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
HALL OF FAMEBLOGOFFLINE CLASS
CHEENTA ON DEMANDBOSE OLYMPIAD
CAREERTEAM
support@cheenta.com