## y = C(n, 7) – floor(n/7)

Show that…

if   $n \; > \; 7$

then,

$\dbinom{ \, n \, }{ \, 7 \, } \; - \; \lfloor n/7 \rfloor$    is divisible by 7

$floor \,(x) \; = \; \lfloor x \rfloor$   is the largest integer not greater than   x   and
$ceiling \,(x) \; = \; \lceil x \rceil$   is the smallest integer not less than   x

$C \, (n, r) \; = \; \dbinom{ \, n \, }{ \, r \, }$   is the number of possible combinations of r objects from a set of n objects.