# Lottery Question

• January 17th 2011, 04:23 AM
slevvio
Lottery Question
I was wondering if anyone had an idea of a strategy I could employ to work out the following question:

Show that less than half of the possible UK lottery selections (six integers from the set $\{1,\ldots,49\}$) contain two consective integers.

It has stumped me and I am not getting anywhere with it. any help would be appreciated thanks. :)
• January 17th 2011, 06:24 AM
Guy
Exactly two consecutive integers, or at least two consecutive integers? If the latter, does a streak of three consecutive integers count?
• January 17th 2011, 06:35 AM
slevvio
the question isn't clear I just copied it. I thought it might be at least two consecutive integers. A streak of 3 would count as 2 pairs of consecutive integers
• January 17th 2011, 07:17 AM
Guy
In that case, count the number total combinations and subtract from that the number of combinations where there are no adjacent integers. That seems to me to be the best way of doing it.