Q.1 9 faculty taking maths, 11 faculty
taking computer science . How many
ways are there to select 7 faculty , 3 from
maths and 4 from computer science
Answers
Step-by-step explanation:
sorry I did not find us this correct
Numberoffacultymembersin
mathemaricsdepartment=9
\begin{gathered} Number \:of \: faculty \: members \: in \\computer\: science \: department = 11 \end{gathered}
Numberoffacultymembersin
computersciencedepartment=11
/* According to the problem given */
Number of ways are there to select a committee to develop a discrete mathematics course at the college if the committee is to consist of three
faculty members from the mathematics department and four from the computer science department = ^{9}C_{3} \times ^{11}C_{4}=
9
C
3
×
11
C
4
\begin{gathered} = \frac{9!}{(9-3)! 3! } \times \frac{11!}{(11-4)! 4! } \\= \frac{9!}{6! 3! } \times \frac{11!}{7! 4! } \\= \frac{9\times 8 \times 7 \times 6!}{6!\times 6} \times \frac{11\times 10 \times 9\times 8\times 7!}{7!\times 24} \end{gathered}
=
(9−3)!3!
9!
×
(11−4)!4!
11!
=
6!3!
9!
×
7!4!
11!
=
6!×6
9×8×7×6!
×
7!×24
11×10×9×8×7!
\begin{gathered} = \frac{9\times 8 \times 7 }{18} \times \frac{11\times 10 \times 9 \times 8 }{24} \\= 28 \times 330 \\= 9240 \end{gathered}
=
18
9×8×7
×
24
11×10×9×8
=28×330
=9240
Therefore.,
\begin{gathered} \red { Number \:ways \:to \:select \:the }\\\red { committee }\green {= 9240 }\end{gathered}
Numberwaystoselectthe
committee=9240