A student is to answer 7 out of 10 questions in an examination. How many choices are there? How many choices are there if at least 3 of the first 5 questions have to be answered? [Hint: split exam into the first 5 and last 5 questions].
A student is to answer 7 out of 10 questions in an examination. How many choices are there? How many choices are there if at least 3 of the first 5 questions have to be answered? [Hint: split exam into the first 5 and last 5 questions].
"At least 3 of the first 5".
We can choose 3 from the first 5, 4 from the first 5, or 5 from the first 5.
That leaves 4 from the remaining 5, 3, and 2 respectively.
$\displaystyle \binom 5 3\cdot\binom 5 4+\binom 5 4\cdot\binom 5 3+\binom 5 5\cdot\binom 5 2$