- #1
Panphobia
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Homework Statement
1)How many bitstring of length 11 contain three more 0's than 1's?
2)How many string of 5 lowercase letters from the Latin alphabet contain:
a) the letter c?
b) the letters c and d?
c) the letters c and d in consecutive positions with c preceding d and all letters distinct?
d) the letters c and d, when c is somewhere to the left of d in the string and all letters are distinct?
The Attempt at a Solution
For 1) I got 11C4
2a) I got 26^5 - 25^5
b) 26^5 - 24^5
c) 4C1*2!*24*23*22/2!... I am not sure at all about this one, my logic is that I take away c and d from the sample size, then divide by 2! to get the arrangement where c is infront of d.
d) 5C2*2*1*24*23*22/2! I am not sure about this one either, I am basically choosing two positions for c and d, subtracting 2 from 26, then multiplying 2*1 to choose from the c and d, then randomly choosing letters for the remaining spots, then dividing by 2! to get the arrangement where c is to the left of d.
Can you guys point out which ones are right and which ones are wrong? Thank you so much.
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