Register

k.Rosen excercise. . How many positive integers less than 1000....

2,050 views
0 votes
0 votes
22. How many positive integers less than 1000

a) have distinct digits?
b) have distinct digits and are even?
User Avatar

2 Answers

1 votes
1 votes

A) total number of integers which are less than 1000 and have distinct digits

                                                 = number of 3 digit numbers which have distinct digits + number of 2 digit numbers which have distinct digits + number of 1 digit numbers which have distinct digits

                                                 = (9*9*8) + (9*9) + 9

                                                 = 648 + 81 + 9

                                                 = 738

B)  total number of integers which are less than 1000 and have distinct digits  and are even

                                                 = number of 3 digit numbers which have distinct digits and are even + number of 2 digit numbers which have distinct digits and are even + number of 1 digit numbers which have distinct digits and are even 

                                                 = [ (9*8*1) + (8*8*4) ]+ [ (9*1) +(8*4) ] + [4]

                                                 = 72 + 256 + 9 + 32 + 4 

                                                 = 373

NOTE :     IN 2 ND QUESTION , I HAVE DIVIDED 3 DIGIT NUMBERS INTO 2 CASES 

                           1) LAST DIGIT IS 0 (HIGHLIGHTED WITH BLUE)

                           2) LAST DIGIT IS NOT 0 

                  SIMILIARLY FOR 2 DIGIT NUMBERS ALSO I HAVE DIVIDED INTO TWO CASES.

  

User Avatar
Voting & Accepting an answer helps improve the community
← PreviousNext →
← Previous in categoryNext in category →

Related questions

5 votes
5 votes
1 answer
1
Vivek sharma asked Jun 28, 2015
4,945 views
How many 4-permutations of the positive integers not exceeding 100 contain three consecutive integers k, k + 1, k + 2,
How many 4-permutations of the positive integers not exceeding 100 contain three consecutive integers k, k + 1, k + 2, in the correct ordera) where these consecutive inte...
User Avatar
1 votes
1 votes
0 answers
3
adarsh shivhare asked Dec 31, 2017
1,109 views
find the number of positive integer less than 91 and relatively prime to 91 ?
User Avatar
5 votes
5 votes
1 answer
4
dd asked Jun 8, 2020
1,204 views
Counting number of pairs whose sum is less than k
How many pairs $(x,y)$ such that $x+y <= k$, where x y and k are integers and $x,y>=0, k > 0$. Solve by summation rules. Solve by combinatorial argument.
How many pairs $(x,y)$ such that $x+y <= k$, where x y and k are integers and $x,y>=0, k 0$.Solve by summation rules.Solve by combinatorial argument.
User Avatar
Link Copied!