Question: 2014 Winter Midterm - 1
On a table, you see three types of fruit: apples, bananas, and oranges. There are $m \geq 2$ apples,
$n \geq 2$ bananas, and $k \geq 2$ oranges. How many ways are there to choose 7 pieces of fruit, if
you must take at least two pieces of each type?
(a)
${m + n + k \choose 7} - {m \choose 2} - {n \choose 2} - {k \choose 2}$
(b)
${m + n + k \choose 7} - (m + n + k)$
(c)
${m \choose 2}{n \choose 2}{k \choose 2}(m + n + k)$
(d)
${m \choose 3}{n \choose 2}{k \choose 2} + {m \choose 2}{n \choose 3}{k \choose 2} + {m \choose 2}{n \choose 2}{k \choose 3}$