Q1. Suppose we have a specially-adapted typewriter for monkeys to use that has o

Question

Q1. Suppose we have a specially-adapted typewriter for monkeys to use that has only 8 keys, one for each of the letters A, B, C,D and W,X, Y, Z Important! All of your solutions must be clearly justified with explanations. (1 pt) a. How many 4-letter "words" can be made using this typewriter? (we consider a 4-letter "word" any ordered string made of 4 (not necessarily distinct) symbols from the type- writer) (2 pts) b. How many 4-letter words are there consisting of 4 distinct letters, one of which is the letter 'A'? (this time, letters may not be repeated) (2 pts) b. Using the monkey typewriter, how many 5-letter words can be made that begin with ABC and end with Z' (letters may be repeated

Explanation / Answer

Solution:

The first four subparts have been answered as per Chegg guidelines, please repost others.

1

a)

out of 8 letters we have to choose 4 letters

so the combination which can be generated is= 8^4

since the repetition is allowed here.

b)

One letter is fixed as A so we have 3 slots to fill to make it 4

so the number of ways will be 7*6*5= 210

c)

Here out of 5, 3 first three slots are fixed with ABC and the last one is fixed with Z

now, only one slot is left and

so 8 letters can be filled in this place in 8 ways.

d)

so we have two cases here

start with ABC, in this the rest two slots can be filled in 64 ways

or end with Z, in this 4 slots can be filled in 8^4 ways

So, total= 8^4 + 64

added later on request:

So N number of monkeys are typing 4 letter world,

so out of these 8 letters total combinations can be 8^4

so if N monkey are typing randomly then 8^4 times they need to enter to see every 4-letter world once

for at least a letter to be repeated twice 3*8^4

The Bonus part:

Yes, there is a minimum valye of N and that will be 8^4.

I hope this helps if you find any problem. Please comment below. Don't forget to give a thumbs up if you liked it. :)

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