Question 1

Find the coeﬃcient of $x ^ { 9 } \text { in the expansion of } \left( 2 + x ^ { 3 } \right) ^ { 10 }$

Accepted Answer

The answer of Find the coeﬃcient of \(x ^ {...

Question 2

Find the number of terms in the expansion of $( 5 a + 8 b ) ^ { 15 }$

Accepted Answer

The answer of Find the number of terms in the...

Question 3

Find the number of permutations of the letters in the word TATTERED.

Accepted Answer

The answer of Find the number of permutations of the...

Question 4

Find the number of permutations of the letters in the word COEFFICIENT.

Accepted Answer

The answer of Find the number of permutations of the...

Question 5

(a) In how many ways are there to arrange the letters of the word NONSENSE ? (b) How many of these ways start or end with the letter O?

Accepted Answer

The answer of (a) In how many ways are there...

Question 6

(a) Find the number of solutions to $x + y + z = 32$ , where $x , y$ ,and $Z$ are nonnegative integers.
(b) Answer part (a), but assume that $x \geq 7$and $y \geq 15$

Accepted Answer

The answer of (a) Find the number of solutions to...

Question 7

You have 50 of each of the following kinds of jellybeans: red, orange, green, yellow. The jellybeans of each color are identical. (a) In how many ways can you put all the jellybeans in a row? (b) How many handfuls of 12 are possible?

Accepted Answer

The answer of You have 50 of each of the...

Question 8

A doughnut shop sells 30 kinds of doughnuts. In how many ways can you (a) get a bag of 12 doughnuts? (b) get a bag of 12 doughnuts if you want at least 3 glazed doughnuts and at least 4 raspberry doughnuts? (c) get a bag of 12 doughnuts if you want exactly 3 glazed doughnuts and exactly 4 raspberry doughnuts?

Accepted Answer

The answer of A doughnut shop sells 30 kinds of...

Question 9

Find the number of permutations of the letters in your last name.

Accepted Answer

The answer of Find the number of permutations of the...

Question 10

assume that you have 50 pennies and three jars, labeled A, B, and C.
-In how many ways can you put the pennies in the jars, assuming that the pennies are identical?

Accepted Answer

The answer of assume that you have 50 pennies and...

Question 11

Find the coeﬃcient of $x ^ { 5 } \text { in } \left( 2 + x ^ { 2 } \right) ^ { 12 } .$

Accepted Answer

The answer of Find the coeﬃcient of \(x ^ {...

Question 12

Find the number of permutations of the letters in the word CORRECT.

Accepted Answer

The answer of Find the number of permutations of the...

Question 13

Find the largest coeﬃcient in the expansion of $( x + 3 ) ^ { 5 }$

Accepted Answer

The answer of Find the largest coeﬃcient in the expansion...

Question 14

You have 20 pennies, 30 nickels, and 40 dimes. Assume that the pennies are identical, the nickels are identical, and the dimes are identical. In how many ways can you put all the coins in a row?

Accepted Answer

The answer of You have 20 pennies, 30 nickels, and...

Question 15

assume that you have 50 pennies and three jars, labeled A, B, and C.
-In how many ways can you put the pennies in the jars, assuming that the pennies are identical and each jar must have at least two pennies put into it?

Accepted Answer

The answer of assume that you have 50 pennies and...

Question 16

Find the number of positive integers not exceeding 1000 that are not divisible by 4, 6, or 9.

Accepted Answer

The answer of Find the number of positive integers not...

Question 17

List the derangements of 1, 2, 3, 4.

Accepted Answer

The answer of List the derangements of 1, 2, 3,...

Question 18

assume that you have 50 pennies and three jars, labeled A, B, and C.
-In how many ways can you put the pennies in the jars, assuming that the pennies are distinguishable?

Accepted Answer

The answer of assume that you have 50 pennies and...

Question 19

How many permutations of 12345 are there that leave 3 in the third position but leave no other integer in its own position?

Accepted Answer

The answer of How many permutations of 12345 are there...

Question 20

How many diﬀerent strings can be made using all the letters in the word GOOGOL?

Accepted Answer

The answer of How many diﬀerent strings can be made...

Quiz 6: A: Counting

Find the coeﬃcient of $x ^ { 9 } \text { in the expansion of } \left( 2 + x ^ { 3 } \right) ^ { 10 }$

Find the number of terms in the expansion of $( 5 a + 8 b ) ^ { 15 }$

Find the number of permutations of the letters in the word TATTERED.

Find the number of permutations of the letters in the word COEFFICIENT.

(a) In how many ways are there to arrange the letters of the word NONSENSE ? (b) How many of these ways start or end with the letter O?

(a) Find the number of solutions to $x + y + z = 32$ , where $x , y$ ,and $Z$ are nonnegative integers. (b) Answer part (a), but assume that $x \geq 7$ and $y \geq 15$

You have 50 of each of the following kinds of jellybeans: red, orange, green, yellow. The jellybeans of each color are identical. (a) In how many ways can you put all the jellybeans in a row? (b) How many handfuls of 12 are possible?

Find the number of permutations of the letters in your last name.

assume that you have 50 pennies and three jars, labeled A, B, and C. -In how many ways can you put the pennies in the jars, assuming that the pennies are identical?

Find the coeﬃcient of $x ^ { 5 } \text { in } \left( 2 + x ^ { 2 } \right) ^ { 12 } .$

Find the number of permutations of the letters in the word CORRECT.

Find the largest coeﬃcient in the expansion of $( x + 3 ) ^ { 5 }$

You have 20 pennies, 30 nickels, and 40 dimes. Assume that the pennies are identical, the nickels are identical, and the dimes are identical. In how many ways can you put all the coins in a row?

assume that you have 50 pennies and three jars, labeled A, B, and C. -In how many ways can you put the pennies in the jars, assuming that the pennies are identical and each jar must have at least two pennies put into it?

Find the number of positive integers not exceeding 1000 that are not divisible by 4, 6, or 9.

List the derangements of 1, 2, 3, 4.

assume that you have 50 pennies and three jars, labeled A, B, and C. -In how many ways can you put the pennies in the jars, assuming that the pennies are distinguishable?

How many permutations of 12345 are there that leave 3 in the third position but leave no other integer in its own position?

How many diﬀerent strings can be made using all the letters in the word GOOGOL?

Quiz 6: A: Counting

Find the coeﬃcient of x9 in the expansion of (2+x3)10x ^ { 9 } \text { in the expansion of } \left( 2 + x ^ { 3 } \right) ^ { 10 }x9 in the expansion of (2+x3)10

Find the number of terms in the expansion of (5a+8b)15( 5 a + 8 b ) ^ { 15 }(5a+8b)15

Find the number of permutations of the letters in the word TATTERED.

Find the number of permutations of the letters in the word COEFFICIENT.

(a) In how many ways are there to arrange the letters of the word NONSENSE ? (b) How many of these ways start or end with the letter O?

(a) Find the number of solutions to x+y+z=32x + y + z = 32x+y+z=32 , where x,yx , yx,y ,and ZZZ are nonnegative integers. (b) Answer part (a), but assume that x≥7x \geq 7x≥7 and y≥15y \geq 15y≥15

You have 50 of each of the following kinds of jellybeans: red, orange, green, yellow. The jellybeans of each color are identical. (a) In how many ways can you put all the jellybeans in a row? (b) How many handfuls of 12 are possible?

Find the number of permutations of the letters in your last name.

assume that you have 50 pennies and three jars, labeled A, B, and C. -In how many ways can you put the pennies in the jars, assuming that the pennies are identical?

Find the coeﬃcient of x5 in (2+x2)12.x ^ { 5 } \text { in } \left( 2 + x ^ { 2 } \right) ^ { 12 } .x5 in (2+x2)12.

Find the number of permutations of the letters in the word CORRECT.

Find the largest coeﬃcient in the expansion of (x+3)5( x + 3 ) ^ { 5 }(x+3)5

You have 20 pennies, 30 nickels, and 40 dimes. Assume that the pennies are identical, the nickels are identical, and the dimes are identical. In how many ways can you put all the coins in a row?

assume that you have 50 pennies and three jars, labeled A, B, and C. -In how many ways can you put the pennies in the jars, assuming that the pennies are identical and each jar must have at least two pennies put into it?

Find the number of positive integers not exceeding 1000 that are not divisible by 4, 6, or 9.

List the derangements of 1, 2, 3, 4.

assume that you have 50 pennies and three jars, labeled A, B, and C. -In how many ways can you put the pennies in the jars, assuming that the pennies are distinguishable?

How many permutations of 12345 are there that leave 3 in the third position but leave no other integer in its own position?

How many diﬀerent strings can be made using all the letters in the word GOOGOL?

Find the coeﬃcient of $x ^ { 9 } \text { in the expansion of } \left( 2 + x ^ { 3 } \right) ^ { 10 }$

Find the number of terms in the expansion of $( 5 a + 8 b ) ^ { 15 }$

(a) Find the number of solutions to $x + y + z = 32$ , where $x , y$ ,and $Z$ are nonnegative integers. (b) Answer part (a), but assume that $x \geq 7$ and $y \geq 15$

Find the coeﬃcient of $x ^ { 5 } \text { in } \left( 2 + x ^ { 2 } \right) ^ { 12 } .$

Find the largest coeﬃcient in the expansion of $( x + 3 ) ^ { 5 }$