(a) How many ways can the letters of the word BECOMING be arranged in a row? (b) How many ways can the letters of the word BECOMING be arranged in a row if B and E must remain next to each other as either BE or EB? A group of seven people is attending the movies together. (a) Two of the seven insist on sitting side-by-side. In how many ways can the seven be seated together in a row? (b) Two of the people do not like each other and do not want to sit side-by-side. Now, how many ways can the seven be seated together in a row? (a) How many integers from 1 through 1,000 are multiples of 4 or multiples of 3? (b) Suppose an integer from 1 through 1,000 is chosen at random. Use the result of part (a) to find the probability that the integer is a multiple of 4 or a multiple of 3. (Round to the nearest tenth of a percent.) (c) How many integers from 1 through 1,000 are neither multiples of 4 nor multiples of 3?
(a) How many ways can the letters of the word BECOMING be arranged in a row? (b) How many ways can the letters of the word BECOMING be arranged in a row if B and E must remain next to each other as either BE or EB? A group of seven people is attending the movies together. (a) Two of the seven insist on sitting side-by-side. In how many ways can the seven be seated together in a row? (b) Two of the people do not like each other and do not want to sit side-by-side. Now, how many ways can the seven be seated together in a row? (a) How many integers from 1 through 1,000 are multiples of 4 or multiples of 3? (b) Suppose an integer from 1 through 1,000 is chosen at random. Use the result of part (a) to find the probability that the integer is a multiple of 4 or a multiple of 3. (Round to the nearest tenth of a percent.) (c) How many integers from 1 through 1,000 are neither multiples of 4 nor multiples of 3?
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.6: Permutations
Problem 39E
Related questions
Concept explainers
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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(a)
How many ways can the letters of the word BECOMING be arranged in a row?
(b)
How many ways can the letters of the word BECOMING be arranged in a row if B and E must remain next to each other as either BE or EB?
A group of seven people is attending the movies together.
(a)
Two of the seven insist on sitting side-by-side. In how many ways can the seven be seated together in a row?
(b)
Two of the people do not like each other and do not want to sit side-by-side. Now, how many ways can the seven be seated together in a row?
(a)
How many integers from 1 through 1,000 are multiples of 4 or multiples of 3?
(b)
Suppose an integer from 1 through 1,000 is chosen at random. Use the result of part (a) to find the probability that the integer is a multiple of 4 or a multiple of 3. (Round to the nearest tenth of a percent.)
(c)
How many integers from 1 through 1,000 are neither multiples of 4 nor multiples of 3?
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