Question

11. Suppose that there are 9 faculty members in the mathematics department and l1 in the com-
puter science department of a college. How many 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 dcpart-
ment?
​

Answer 1

$Number \:of \: faculty \: members \: in \\mathemarics \: department = 9$

$Number \:of \: faculty \: members \: in \\computer\: science \: department = 11$

/* 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 $= ^{9}C_{3} \times ^{11}C_{4}$

$= \frac{9!}{(9-3)! 3! } \times \frac{11!}{(11-4)! 4! } \\= \frac{9!}{6! 3! } \times \frac{11!}{7! 4! } \\= \frac{9\times 8 \times 7 \times 6!}{6!\times 6} \times \frac{11\times 10 \times 9\times 8\times 7!}{7!\times 24}$

$= \frac{9\times 8 \times 7 }{18} \times \frac{11\times 10 \times 9 \times 8 }{24} \\= 28 \times 330 \\= 9240$

Therefore.,

$\red { Number \:ways \:to \:select \:the }\\\red { committee }\green {= 9240 }$

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Answer 2

my answer is 330 this is so easy problem you can solve