Thursday

April 24, 2014

April 24, 2014

Posted by **carlton** on Sunday, April 8, 2012 at 2:04pm.

(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

= 286-29=257

(b) distinct digits

First digit has 9 choices (1-9)

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= (10000-1000)/5=1800

Divisisble by 7, n7 = (10003-1001)/7=1286

Divisible by 5 or 7 or both

=n5+n7-n35

=1800+1286-257

=2829

Numbers NOT divisible by either 5 or 7

=(10000-1000)-2829

=6171

**Related Questions**

Discrete Math - Theorem: For every integer n, if x and y are positive integers ...

math - Find the sum of all positive integers m such that 2^m can be expressed as...

math - Find the sum of all positive integers m such that 2^m can be expressed as...

math - Find the sum of all positive integers m such that 2^m can be expressed as...

discrete math - let d be a positive integer. Show that among any group of d+...

Discrete Math - Let n be positive integer greater than 1. We call n prime if the...

Peter - For all positive integers w and y, where w > y, let the operation &#...

math - The four values x, y, x−y and x+y are all positive prime integers. ...

math - the sum of the squares of four consecutive positive integers is 734. what...

discrete math - 1)prove that if x is rational and x not equal to 0, then 1/x is ...