Problem
COM-B1-M03-P022 Five Numbers Without Adjacency and with One
#22
★★★★☆ Level 4 of 5
How many \(5\)-element subsets of \(\{1,\ldots,15\}\) contain \(1\) and contain no consecutive numbers?
If \(1\) is chosen, \(2\) is forbidden.
After choosing \(1\), choose \(4\) more numbers from \(\{3,\ldots,15\}\) with no adjacency. This is an interval of length \(13\). The number of ways to choose \(4\) nonconsecutive elements from \(13\) is \(\binom{13-4+1}{4}=\binom{10}{4}=210\).
Shift method with an extra condition.