Exam 6: A: Counting

suppose you have 30 books (15 novels, 10 history books, and 5 math books). Assume that all 30 books are different. -In how many ways can you get a bunch of three history books and seven novels to give to a friend?

suppose that a "word" is any string of seven letters of the alphabet, with repeated letters allowed. -How many words are there?

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

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?

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?

suppose you have 30 books (15 novels, 10 history books, and 5 math books). Assume that all 30 books are different. -In how many ways can you put the 30 books in a row on a shelf if the novels are on the left, the math books are in the middle, and the history books are on the right?

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?

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?

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

a club with 20 women and 17 men needs to form a committee of size six. -How many committees are possible if the committee must consist of all women or all men?

Rental cars belong to one of twelve classifications depending on size and type of car. Each car is also assigned one of six color categories. How many cars does a rental agency need to guarantee that there are at least two cars of the same classification and color?

suppose that a "word" is any string of seven letters of the alphabet, with repeated letters allowed. -How many words have no vowels?

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?

Find the next largest permutation in lexicographic order after 1324.

Make up a word problem in good English whose answer is $15 ! / 10 !$

consider all bit strings of length 12. -How many have exactly four 1's?

let A be the set of all strings of decimal digits of length five. For example, 00312 and 19483 are strings in A. -How many strings in A begin with 774?

If the permutations of 1, 2, 3, 4, 5, 6 are written in lexicographic order, with 123456 in position #1, 123465 in position #2, etc., find the permutation immediately after 246531.

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?

suppose you have a class with 30 students-10 freshmen, 12 sophomores, and 8 juniors. -In how many ways can you get a committee of 4 freshmen and 3 sophomores?