Question 1

In questions nine people (Ann, Ben, Cal, Dot, Ed, Fran, Gail, Hal, and Ida) are in a room. Five of
them stand in a row for a picture.
-In how many ways can this be done if Ed and Gail are in the picture, standing next to each other?

Accepted Answer

The answer of In questions nine people (Ann, Ben, Cal,...

Question 2

How many permutations of the seven letters A, B, C, D, E, F, G neither begin nor end with A?

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The answer of How many permutations of the seven letters...

Question 3

In questions nine people (Ann, Ben, Cal, Dot, Ed, Fran, Gail, Hal, and Ida) are in a room. Five of
them stand in a row for a picture.
-In how many ways can this be done if both Ed and Gail are in the picture?

Accepted Answer

The answer of In questions nine people (Ann, Ben, Cal,...

Question 4

In questions nine people (Ann, Ben, Cal, Dot, Ed, Fran, Gail, Hal, and Ida) are in a room. Five of
them stand in a row for a picture.
-In how many ways can this be done if Dot is on the left end and Ed is on the right end?

Accepted Answer

The answer of In questions nine people (Ann, Ben, Cal,...

Question 5

How many 5-element DNA sequences use all four bases, A, T, C, and G?

Accepted Answer

The answer of How many 5-element DNA sequences use all...

Question 6

In questions let A be the set of all bit strings of length 10.
-How many bit strings of length 10 are there?

Accepted Answer

The answer of In questions let A be the set...

Question 7

How many permutations of the seven letters A, B, C, D, E, F, G do not have vowels on the ends?

Accepted Answer

The answer of How many permutations of the seven letters...

Question 8

In questions nine people (Ann, Ben, Cal, Dot, Ed, Fran, Gail, Hal, and Ida) are in a room. Five of
them stand in a row for a picture.
-In how many ways can this be done if Ben is to be in the picture?

Accepted Answer

The answer of In questions nine people (Ann, Ben, Cal,...

Question 9

In questions nine people (Ann, Ben, Cal, Dot, Ed, Fran, Gail, Hal, and Ida) are in a room. Five of
them stand in a row for a picture.
-In how many ways can this be done if neither Ed nor Fran are in the picture?

Accepted Answer

The answer of In questions nine people (Ann, Ben, Cal,...

Question 10

How many permutations of the seven letters A, B, C, D, E, F, G have the two vowels before the ﬁve consonants?

Accepted Answer

The answer of How many permutations of the seven letters...

Question 11

How many permutations of the seven letters A, B, C, D, E, F, G have A immediately to the left of E?

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Question 12

In a technician's box there are 400 VLSI chips, 12 of which are faulty. How many ways are there to pick two
chips, so that one is a working chip and the other is faulty? (Assume that no chips are identical.)

Accepted Answer

The answer of In a technician's box there are 400...

Question 13

How many 8-element DNA sequences start with C and end with C?

Accepted Answer

The answer of How many 8-element DNA sequences start with...

Question 14

How many 8-element DNA sequences contain exactly four C's?

Accepted Answer

The answer of How many 8-element DNA sequences contain exactly...

Question 15

In questions nine people (Ann, Ben, Cal, Dot, Ed, Fran, Gail, Hal, and Ida) are in a room. Five of
them stand in a row for a picture.
-In how many ways can this be done if Hal or Ida (but not both) are in the picture?

Accepted Answer

The answer of In questions nine people (Ann, Ben, Cal,...

Question 16

How many permutations of the seven letters A, B, C, D, E, F, G do not have the vowels next to each other?

Accepted Answer

The answer of How many permutations of the seven letters...

Question 17

In questions nine people (Ann, Ben, Cal, Dot, Ed, Fran, Gail, Hal, and Ida) are in a room. Five of
them stand in a row for a picture.
-In how many ways can this be done if Ann and Ben are in the picture, but not standing next to each other?

Accepted Answer

The answer of In questions nine people (Ann, Ben, Cal,...

Question 18

How many 8-element DNA sequences contain exactly two of the four bases?

Accepted Answer

The answer of How many 8-element DNA sequences contain exactly...

Question 19

How many truth tables are possible for compound propositions with the ﬁve variables p, q, r, s, t ?

Accepted Answer

The answer of How many truth tables are possible for...

Question 20

How many permutations of the seven letters A, B, C, D, E, F, G have E in one of the ﬁrst two positions?

Accepted Answer

The answer of How many permutations of the seven letters...

Quiz 6: Counting

In questions nine people (Ann, Ben, Cal, Dot, Ed, Fran, Gail, Hal, and Ida) are in a room. Five of them stand in a row for a picture. -In how many ways can this be done if Ed and Gail are in the picture, standing next to each other?

How many permutations of the seven letters A, B, C, D, E, F, G neither begin nor end with A?

In questions nine people (Ann, Ben, Cal, Dot, Ed, Fran, Gail, Hal, and Ida) are in a room. Five of them stand in a row for a picture. -In how many ways can this be done if both Ed and Gail are in the picture?

In questions nine people (Ann, Ben, Cal, Dot, Ed, Fran, Gail, Hal, and Ida) are in a room. Five of them stand in a row for a picture. -In how many ways can this be done if Dot is on the left end and Ed is on the right end?

How many 5-element DNA sequences use all four bases, A, T, C, and G?

In questions let A be the set of all bit strings of length 10. -How many bit strings of length 10 are there?

How many permutations of the seven letters A, B, C, D, E, F, G do not have vowels on the ends?

In questions nine people (Ann, Ben, Cal, Dot, Ed, Fran, Gail, Hal, and Ida) are in a room. Five of them stand in a row for a picture. -In how many ways can this be done if Ben is to be in the picture?

In questions nine people (Ann, Ben, Cal, Dot, Ed, Fran, Gail, Hal, and Ida) are in a room. Five of them stand in a row for a picture. -In how many ways can this be done if neither Ed nor Fran are in the picture?

How many permutations of the seven letters A, B, C, D, E, F, G have the two vowels before the ﬁve consonants?

How many permutations of the seven letters A, B, C, D, E, F, G have A immediately to the left of E?

In a technician's box there are 400 VLSI chips, 12 of which are faulty. How many ways are there to pick two chips, so that one is a working chip and the other is faulty? (Assume that no chips are identical.)

How many 8-element DNA sequences start with C and end with C?

How many 8-element DNA sequences contain exactly four C's?

In questions nine people (Ann, Ben, Cal, Dot, Ed, Fran, Gail, Hal, and Ida) are in a room. Five of them stand in a row for a picture. -In how many ways can this be done if Hal or Ida (but not both) are in the picture?

How many permutations of the seven letters A, B, C, D, E, F, G do not have the vowels next to each other?

In questions nine people (Ann, Ben, Cal, Dot, Ed, Fran, Gail, Hal, and Ida) are in a room. Five of them stand in a row for a picture. -In how many ways can this be done if Ann and Ben are in the picture, but not standing next to each other?

How many 8-element DNA sequences contain exactly two of the four bases?

How many truth tables are possible for compound propositions with the ﬁve variables p, q, r, s, t ?

How many permutations of the seven letters A, B, C, D, E, F, G have E in one of the ﬁrst two positions?