Solution to (a) How many code words over a, b, c, d of length 20 contain exactly … - Sikademy
Author Image

Archangel Macsika

(a) How many code words over a, b, c, d of length 20 contain exactly 10 a’s? (b) How many contain exactly 10 a’s and 5b’s.

The Answer to the Question
is below this banner.

Can't find a solution anywhere?

NEED A FAST ANSWER TO ANY QUESTION OR ASSIGNMENT?

Get the Answers Now!

You will get a detailed answer to your question or assignment in the shortest time possible.

Here's the Solution to this Question

(a) Remaining 20-10=10 places to be filled with b,c,d. Each of these places can be filled in 3 ways. Hence total number of ways of filling is 3^{10}. Out of 20 places 10 places can be chosen in (\begin{matrix} 20\\ 10 \end{matrix}) ways. Hence answer is 3^{10}(\begin{matrix} 20\\ 10 \end{matrix}) .

(b) Here as before we need to fill 5 places with c and d. This can be done in 2^5 ways. The 5 places can be chosen in (\begin{matrix} 20\\ 5 \end{matrix}) ways. Now a and b with first one 10 times repeated and b 5 times repeated can be done in \frac{15!}{10!5!} ways. Hence no of words is 2^5 (\begin{matrix} 20\\ 5 \end{matrix}) \frac{15!}{10!5!} ways.

Related Answers

Was this answer helpful?

Join our Community to stay in the know

Get updates for similar and other helpful Answers

Question ID: mtid-5-stid-8-sqid-3007-qpid-1706