Posted by carlton on Sunday, April 8, 2012 at 2:04pm.
Find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, have the following properties:
(a) are divisible by 5 and by 7.
(b) have distinct digits.
(c) are not divisible by either 5 or 7.

discrete math  MathMate, Sunday, April 8, 2012 at 3:47pm
(a) div. by 5 and by 7 => div. by 35
We can find out that
35*286=10010 and 35*29=1015
Therefore the number divisible by 35, n35
= 28629=257
(b) distinct digits
First digit has 9 choices (19)
second and subsequent digits 9,8,7 choices each
Numbers with distinct digits
= 9*9*8*7
= 4536
(c) not divisible by either 5 or 7
Divisible by 5, n5= (100001000)/5=1800
Divisisble by 7, n7 = (100031001)/7=1286
Divisible by 5 or 7 or both
=n5+n7n35
=1800+1286257
=2829
Numbers NOT divisible by either 5 or 7
=(100001000)2829
=6171
Answer This Question
Related Questions
 DISCRETE MATH  HOW MANY POSITIVE INTEGERS LESS THAN 1000 A.are divisible by ...
 calculus  A positive multiple of 11 is good if it does not contain any even ...
 Arithmetic Operations  Find a set of 4 distinct positive integers a,b,c,d such ...
 discrete math  How many strings of four decimal digits (Note there are 10 ...
 math  Find the sum of all positive integers m such that 2^m can be expressed as...
 Discrete Math  Theorem: For every integer n, if x and y are positive integers ...
 Integers  Integers greater than 1000 are created using the digits 2, 0, 1, 4 ...
 Algebra  Joe picks 2 distinct numbers from the set of the first 14 positive ...
 MATH  Let’s agree to say that a positive integer is primelike if it is not ...
 math  Let’s agree to say that a positive integer is primelike if it is not ...
More Related Questions