Cheenta

Academy for Gifted Students

How Cheenta works to ensure student success?

Explore the Back-StoryThis is a Test of Mathematics Solution Subjective 60 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.

Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta

Consider the set S of all integers between and including 1000 and 99999. Call two integers x and y in S to be in the same equivalence class if the digits appearing in x and y are the same. For example, if x = 1010, y = 1000 and z = 1201, then x and y are in the same equivalence class, but y and z are not. Find the number of distinct equivalence classes that can be formed out of S.

Any set of distinct digits with maximum order 5 is a equivalence class that can be formed out of S except {0}.

Number of such sets is

= $ { {10} \choose {1}} $ + $ { {10} \choose {2}} $ + $ {{10} \choose {3}} $ + $ { {10}\choose{4}} $ + $ {{10}\choose{5}} $ -1

= 10 + 45 + 120 + 210 + 252 -1

= 636

This is a Test of Mathematics Solution Subjective 60 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.

Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta

Consider the set S of all integers between and including 1000 and 99999. Call two integers x and y in S to be in the same equivalence class if the digits appearing in x and y are the same. For example, if x = 1010, y = 1000 and z = 1201, then x and y are in the same equivalence class, but y and z are not. Find the number of distinct equivalence classes that can be formed out of S.

Any set of distinct digits with maximum order 5 is a equivalence class that can be formed out of S except {0}.

Number of such sets is

= $ { {10} \choose {1}} $ + $ { {10} \choose {2}} $ + $ {{10} \choose {3}} $ + $ { {10}\choose{4}} $ + $ {{10}\choose{5}} $ -1

= 10 + 45 + 120 + 210 + 252 -1

= 636

Cheenta is a knowledge partner of Aditya Birla Education Academy

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

JOIN TRIALAcademic Programs

Free Resources

Why Cheenta?

Online Live Classroom Programs

Online Self Paced Programs [*New]

Past Papers

More