# Simple( discrete maths)

• May 19th 2009, 12:47 PM
lat87
Simple( discrete maths)
This is meant to be a very simple question and i am sure it is however once a few of us have come togther to share answers there has been a disagreement so we needed some help.

Q) Find in how many ways three distinct numbers can be chosen from
{1,2,3,4,5,6,7,8,9,10}
so that no two are consectutive..
• May 19th 2009, 12:54 PM
Plato
Quote:

Originally Posted by lat87
Q) Find in how many ways three distinct numbers can be chosen from
{1,2,3,4,5,6,7,8,9,10}
so that no two are consectutive..

How many ways are there to arrange the string '1110000000' so no two 1's are together?
You could have 0100100001. That represents {2,5,10}.
You cannot have 0011001000. That represents {3,4,7}.
• May 19th 2009, 01:28 PM
lat87
thankyou for taking the time to look over question.
i was just wondering..
the answer i have was 79 which i got using 120-48+7

if this correct?
once again many thanks
• May 19th 2009, 01:37 PM
Plato
Quote:

Originally Posted by lat87
thankyou for taking the time to look over question.
i was just wondering..
the answer i have was 79 which i got using 120-48+7 if this correct?

No. The answer is the one I gave.
How many ways can a string of seven zeros and three one be arranged so no two ones are together.
$\binom{8}{3} =56$

_0_0_0_0_0_0_0_ there are eight places to put the 1's.
• May 19th 2009, 01:43 PM
TiRune
No use reposting the question, it was already solved a thread below. I made an arithmetic mistake prolly due to lack of coffee. The method however was correct and you can apply it yourself. Plato's method is also very valid and results in the same answer.