Answer: a) 3876 b) 18480
Step-by-step explanation:
Given , The number of professors = 8
The number of students are available = 11
Total persons = 8+11=19
a) The number of ways to select 4 people = [tex]^{19}C_{4}[/tex]
[tex]=\dfrac{19!}{4!(19-4)!}\ \ \ [\because\ ^nC_r=\dfrac{n!}{r!(n-r)!}]\\=\dfrac{19\times18\times17\times16\times15!}{24\times15!}\\=3876[/tex]
Hence, the number of ways to select 4 people = 3876.
b) Number of ways to choose 3 professors and 4 students = [tex]^{8}C_{3}\times^{11}C_{4}[/tex]
[tex]=\dfrac{8!}{3!(8-3)!}\times\dfrac{11!}{4!(11-4)!}\\\\=56\times330\\\\=18480[/tex]
Hence, the numbers of ways to form a committee with 3 professors and 4 students = 18480.
