a        A box contains large numbers of red, blue and green counters. Some are taken out.

i         The following two statements about the counters that are taken out are both true:

“there are only two which are not red”,

“there are only three which are not green”.

Show that there are only three different possible combinations of counters that might have been taken out.

ii        If the following two statements about the counters that are taken out are both true, how many different combinations of counters could there have been, in terms of m  and n?

“there are only n which are not red”,

“there are only m which are not green”.

 

b       A box contains large numbers of red, blue, green and yellow counters. Some are taken out.

i         If the following two statements about the counters that are taken out are both true, how many different combinations of counters could there have been, in terms of n?

“there are only n which are not red”,

“there are only n which are not green”.

ii        If the following three statements about the counters that are taken out are both true, how many different combinations of counters could there have been, in terms of n?

“there are only n which are not red”,

“there are only n which are not yellow”,

“there are only n which are not green”.