Question

I need to verify and correct these exercises

3. A conference offers 3 seminars at 9:00 am, 5 seminars at 10:00 am, and 4 seminars at 11:00 am. You also have the option of not attending a seminar at any given hour. How many different ways can you spend your morning at the conference?

The number of choices to attend the conference at 9:00AM is 3.

The number of choices to attend the conference at 10:00AM is 5.

The number of choices to attend the conference at 11:00AM is 4.

The total number of choices is 3 × 5 × 4 = 60

5. How many 5-character sequences consist of two letters followed by 3 digits with no character being repeated?

The number of 5-character sequences consists of two letters followed by 3 digits with no character being repeated is 26 × 25 × 10 × 10 × 10 = 650,000

8. Suppose that a quiz in a discrete mathematics course consists of 15 questions. How many different sequences of answers are possible for this quiz if a) each question is a true-false question? b) each question is a multiple-choice question with 4 possible answers?

a) Suppose that a quiz in a discrete mathematics course consists of 15 questions Each question is a true-false question. Hence for each question, we have two chances. The total number of chances to answer the 15 questions is 15 x 2 = 30

b) Suppose each question has four possible answers. Then the total number of chances to answer the 15 questions is 15 x 4 = 60

10. A student is preparing to go to class on a winter morning. He has three coast, four sweaters and two hats. How many possibilities does he have of what to wear if he must wear a coat?

No of coats 3

Sweaters 4

Hats 2

As coat is fixed he has 4 choices for sweaters and 2 for hats

Hence no of possibilities = 4x2 = 8

Answer 1

3
The answer will be 4*6*5=120
because the user can also skip any of the conference, you need to account for that also

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5
If you are considering only UPPER CASE or LOWER CASE letter then your answer is correct
If you can use both upper case and lower letters then the answer will be
52*51*50*10*10*10

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8
a) each question is a true-false question?
it will be 2^15=32768
first question can be true or false - 2 options
second question can be true or false - 2 options
..
..
15th question can be true or false - 2 options
so total possibilities 2*2*2.....*2=32768

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b) each question is a multiple-choice question with 4 possible answers?
4^15 = 1,073,741,824

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10
he can wear a sweater or not wear it so there are 1+4=5 possibilities
he can wear a hat or not wear it so there are 1+2=3 possibilities
total combinations between sweater and hat = 5*3=15

Now, for each coat we can have 15 combinations of sweater and hat
so for 3 coats we will have 3*15=45 combinations

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