Question

How many 5-element DNA sequences

a) end with A?

b) start with T and end with G?

c) contain only A and T?

d) do not contain C?

Hint: Recall that a DNA sequence is a sequence of letters,
each of which is one of A, C, G, or T. Thus by the product

rule there are 4^5 = 1024 DNA sequences of length five if we
impose no restrictions.

discrete math

discrete structures

Answer #1

DEFINITIONS

**Product rule** If one event can occur in m ways AND
a second event can occur in n ways, the number of ways the two
events can occur in sequence is then m • n.

**Sum rule** If an event can occur either in m ways OR
in n ways (non-overlapping), the number of ways the event can occur
is then m + n.

**Subtraction rule** If an event can occur either in m
ways OR in n ways (overlapping), the number of ways the event can
occur is then m + n decreased by the number of ways that the event
can occur commonly to the two different ways.

SOLUTION

There are 4 possible DNA bases: A, C, G and T

(a)

First base: 4 ways

Second base: 4 ways

Third base: 4 ways

Fourth base: 4 ways

Fifth base: 1 way (since it has to be A)

We need to use the product rule, because the first event is picking the first base, the second event is picking the second base, ...., the 5th event is picking the 5th base.

4.4.4.4.1 = 256

(b)

First base: 1 way (since it has to be T)

Second base: 4 ways

Third base: 4 ways

Fourth base: 4 ways

Fifth base: 1 way (since it has to be G)

We need to use the product rule, because the first event is picking the first base, the second event is picking the second base, ...., the 5th event is picking the 5th base.

1.4.4.4.1 = 64

(c)

First base: 2 ways (since it has to be A or T)

Second base: 2 ways (since it has to be A or T)

Third base: 2 ways (since it has to be A or T)

Fourth base: 2 ways (since it has to be A or T)

Fifth base: 2 ways (since it has to be A or T)

We need to use the product rule, because the first event is picking the first base, the second event is picking the second base, ...., the 5th event is picking the 5th base.

2.2.2.2.2 = 32

(d)

First bane: 3 ways (since it cannot be C)

Second base: 3 ways (since it cannot be C)

Third base: 3 ways (since it cannot be C)

Fouth base: 3 ways (since it cannot be C)

Fifth base: 3 ways (since it cannot be C)

We need to use the product rule, because the first event is picking the first bane, the second event is picking the second base, ...., the 5th event is picking the 5th base.

3.3.3.3.3 = 243

**RESULT**

(a) 256 DNA sequences

(d) 64 DNA sequences

(c) 32 DNA sequences

(d) 243 DNA sequences

How many 5-element DNA sequences
a) end with A?
b) start with T and end with G?
c) contain only A and T?
d) do not contain C?
Hint: Recall that a DNA sequence is a sequence of letters,
each of which is one of A, C, G, or T. Thus by the product
rule there are 4^5 = 1024 DNA sequences of length five if we
impose no restrictions.
discrete strctures

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?

Please summarize the below article in approximately 100
words:
Monumental function in British Neolithic burial practices
Ian Kinnes
The high-risk rate of survival for the non-megalithic series of
Neolithic funerary monuments, recently re-emphasized by Piggott
(1973: 34), introduces a further variable into the deductive study
of burial practices. In Britain and Europe the overall distribution
of monumental forms present both lacunae and a marked preponderance
of cairns over earthen mounds which are in ill accord with the
known or predicted...

Using the model proposed by Lafley and Charan, analyze how
Apigee was able to drive innovation.
case:
W17400
APIGEE: PEOPLE MANAGEMENT PRACTICES AND THE CHALLENGE OF
GROWTH
Ranjeet Nambudiri, S. Ramnarayan, and Catherine Xavier wrote
this case solely to provide material for class discussion. The
authors do not intend to illustrate either effective or ineffective
handling of a managerial situation. The authors may have disguised
certain names and other identifying information to protect
confidentiality.
This publication may not be...

The Business Case for Agility
“The battle is not always to the strongest, nor the
race to the swiftest, but that’s the way to bet
’em!” —C. Morgan Cofer
In This Chapter
This chapter discusses the business case for Agility,
presenting six benefits for teams and the enterprise. It also
describes a financial model that shows why incremental development
works.
Takeaways
Agility is not just about the team. There are
product-management, project-management, and technical issues beyond
the team’s control. Lean-Agile provides...

Please answer the following Case
analysis questions
1-How is New Balance performing compared to its primary rivals?
How will the acquisition of Reebok by Adidas impact the structure
of the athletic shoe industry? Is this likely to be favorable or
unfavorable for New Balance?
2- What issues does New Balance management need to address?
3-What recommendations would you make to New Balance Management?
What does New Balance need to do to continue to be successful?
Should management continue to invest...

Delta airlines case study
Global strategy. Describe the current global
strategy and provide evidence about how the firms resources
incompetencies support the given pressures regarding costs and
local responsiveness. Describe entry modes have they usually used,
and whether they are appropriate for the given strategy. Any key
issues in their global strategy?
casestudy:
Atlanta, June 17, 2014. Sea of Delta employees and their
families swarmed between food trucks, amusement park booths, and
entertainment venues that were scattered throughout what would...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 7 minutes ago

asked 8 minutes ago

asked 8 minutes ago

asked 11 minutes ago

asked 13 minutes ago

asked 14 minutes ago

asked 26 minutes ago

asked 40 minutes ago

asked 48 minutes ago

asked 48 minutes ago

asked 57 minutes ago

asked 58 minutes ago