Please answer as many as possible. Thank you so much! 2. An office building cont
ID: 3852817 • Letter: P
Question
Please answer as many as possible. Thank you so much!
2. An office building contains 27 floors and has 37 offices on each floor. How many offices are in the building? 4. A particular brand of shirt comes in 12 colors, has a male version and a female version, and comes in three sizes for each sex. How many different types of this shirt are made? 6. There are four major auto routes from Boston to Detroit and six from Detroit to Los Angeles. How many major auto routes are there from Boston to Los Angeles via De- troit? 8. How many different three-letter initials with none of the 12. How many bit strings are there of length six or less, not 14. How many bit strings of length n, where n is a positive 16. How many strings are there of four lowercase letters that 20. How many positive integers between 5 and 31 letters repeated can people have? counting the empty string? integer, start and end with ls? have the letter x in them? a) are divisible by 3? Which integers are these? b) are divisible by 4? Which integers are these? c) are divisible by 3 and by 4? Which integers are these?Explanation / Answer
2) total number of offices in the building are 27*37=999
4) number of shirts are: 12*2*3=72 ( 12 diff Colors *(1 men+1 women)*3sizes)
6) major auto routes are: 4*6=24
8) number of three letter initials are : 26*25*24=15600
12) number of bit strings are: 2^6+2^5+2^4+2^3+2^2+2^1= 64+32+16+8+4+2=126
14) for n=1 one bit string of length n=1
For n>2 1*2*2*......2*1=2^(n-2)
16) number of strings are: 4*26^3= 70304
20) a) number of positive integers that are divisible by 3 are 6,9,12,15,18,21,24,27,30
b) divisible by 4 are: 8,12,16,20,24,28
C) divisible by both 3,4 are: we do not have any positive integers that are divisible by both 3,4
26) a)first digit has 10 possibilities second has 9 and third has 8 and fourth has 7 possibilities. So totally 10*9*8*7=5040
b) first 3 digits have 10 possibilities,last have 5 totally 10*10*10*5=5000
C) 9 digit can be anywhere in the four places. And other is not 9 digit so totally 9*4=36
46) a) bride position is fixed so the answer is 6!*9C5
b) bride and groom position fixed so answer is 8C4*6!
c) the possible arrangements are : 2*8C5*6!
48) if first 2 bits are 0's then 5 bits are free= 2^5
If last 3 bits are filled by 1 then we have 2^4= 16 bits
If first 2 bits and last 3 bits are filled the remaining are 2^4
So totally: 32+16-4=44
52) (38+23)-7=54 students
54) 26^5+26^4+26^3+26^2
56) 26 upper+ 26 lower letters totally 52+ Underscore+10 digits=63
Length 1 - 53
Length 2 - 53*63
Length 3 - 53*63^2
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.
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Total 53+53*63+53*63^2+...+53*63^7
62) p and q are primes so the only integer included in the sets are pq= qp= n
By inclusion-exclusion principle the number of Integers not exceeding n which are not relatively prime to n is p+q-1
The answer is : n-(p+q-1)