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.
What is the number of 6 digit positive integers in which the sum of the digits is at least 52?
Basic counting principles
Answer: is
ISI MStat 2019 PSA Problem 4
A First Course in Probability by Sheldon Ross
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 .
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's M.Stat Entrance. They ranked within the first 50 in the entire country in these entrances. I.S.I. M.Stat Entrance
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's B.Stat Entrance and Chennai Mathematical Institute's B.Sc. Math Entrance. They ranked within the first 200 in the entire country in these entrances. Most of these students attended the problem solving workshops regularly, which happen 5 days every week. CMI B.Sc. Math Entrance […]
In 2025, 8 students from Cheenta Academy cracked the prestigious Regional Math Olympiad. In this post, we will share some of their success stories and learning strategies. The Regional Mathematics Olympiad (RMO) and the Indian National Mathematics Olympiad (INMO) are two most important mathematics contests in India.These two contests are for the students who are […]
Cheenta Academy proudly celebrates the success of 27 current and former students who qualified for the Indian Olympiad Qualifier in Mathematics (IOQM) 2025, advancing to the next stage — RMO. This accomplishment highlights their perseverance and Cheenta’s ongoing mission to nurture mathematical excellence and research-oriented learning.
