4.08: Counting numbers and committees

0606/22/M/J/26 — Question 5 · 6 marks

(a)
Find how many six-digit numbers with six different digits, not beginning with \(0\), are divisible by \(2\).
[3]
(b)
A committee of \(10\) is chosen from \(9\) students and \(7\) teachers. Find how many committees contain at least \(4\) students and at least \(4\) teachers.
[3]