Answer to Question #98475 in Discrete Mathematics for Ahmed

Question #98475
In an exam, a student is required to answer 10 out of 13 questions. Find the number of
possible choices if the student must answer:
(a) the first two questions;
(b) the first or second question, but not both;
(c) exactly 3 out of the first 5 questions;
(d) at least 3 out of the first 5 questions.
1
Expert's answer
2019-11-12T10:59:22-0500

a)

The student MUST answer to the first 2 questions. These two questions are not fit to be chosen. So we have 13-2=11 questions left, and 10-2=8 questions left to be chosen.


"n=\\binom{13-2}{10-2}={11! \\over 8!(11-8)!}={11(10)(9) \\over 1(2)(3)}=165"

b)

One question, the first or the second, has been answered. So we have 13-1=12 questions left, and we have to answer to 10-1=9 questions.


"n=\\binom{2}{1}\\binom{13-2}{10-1}=2\\cdot{11! \\over 9!(11-9)!}=2\\cdot{11(10) \\over 1(2)}=110"

c)


"n=\\binom{5}{3}\\binom{13-5}{10-3}={5! \\over 3!(5-3)!}\\cdot{8! \\over 7!(8-7)!}=10\\cdot8=80"


d)


"n=\\binom{5}{3}\\binom{13-5}{10-3}+\\binom{5}{4}\\binom{13-5}{10-4}+\\binom{5}{5}\\binom{13-5}{10-5}"

"={5! \\over 3!(5-3)!}\\cdot{8! \\over 7!(8-7)!}+{5! \\over 4!(5-4)!}\\cdot{8! \\over 6!(8-6)!}+{5! \\over 5!(5-5)!}\\cdot{8! \\over 5!(8-5)!}"


"=10(8)+5(28)+1(56)=276"


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS