Question

# Discrete Math a.) How many bit strings are there of length five or less, not counting...

Discrete Math

a.) How many bit strings are there of length five or less, not counting the empty string?

b.) How many different three-letter initials with none of the letters repeated can people have?

c.) How many different three-letter initials are there that begin with the letter B?

d.) How many 5-element DNA sequences end with A?

e.) How many bit strings of length nine both begin and end with 1?

a) number of bit strings of length five or less is 2^5 + 2^4 + 2^3+2^2+2^1 =32+16+8+4+2

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b)first letter can be chosen from 26 lettters

second letters can be chosen from 25 letters

third letter can be chosen from 24 letters

so total = 26*25*24=15,600

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C) first letter is fixed that is B=1

second and third can be choosen from 26 letters

so total =1*26*26= 676

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d) Given five element DNA sequences.

The possible dna bases are A,C,G and T

the fourst four bases can be picked from the 4 letters (A,C,T,G)

and the last letter should be only A

so total = 4*4*4*4*1 = 64

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E) first bt should always be 1 and last bit should always be 1.

From second to eight bit we can choose either 0 or 1

so tota =1*2*2*2*2*2*2*2*1 =2^7 = 128

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