MATH SOLVE

5 months ago

Q:
# ) In how many ways can 5 different novels, 2 different mathematics books, and 1 biology book be arranged on a bookshelf if (a) the books can be arranged in any order? Answer: 40320 (b) the mathematics books must be together and the novels must be together? Answer: (c) the mathematics books must be together but the other books can be arranged in any order? Answer:

Accepted Solution

A:

Answer:a. 40320b. 1440c. 10080Step-by-step explanation:Number of Novels: 5Numbers of Mathematics books: 2Number of biology: 1a. If the books are to be arranged in any orderTotal number of books = 5 + 2 + 1 = 8Number of Arrangements = 8!Number of Arrangements = 8*7*6*5*4*3*2*1Number of Arrangements = 40320 waysb. The mathematics books must be together and the novels must be togetherTo get the number of possible arrangementsFirst, Calculate the Possible Arrangements of Mathematics Books;Number of Mathematics Books = 2Arrangements = 2!Arrangements = 2*1 = 2Then, Calculate the Possible Arrangements of Novel Books;Number of Novel Books = 5Arrangements = 5!Arrangements = 5*4*3*2*1Arrangements = 120Then Calculate the Possible Arrangements of the Mathematics book bundle, Novel Bundle with Biology book.The mathematics book bundled together is 1The novel bundled together is 1Other books = 1 BiologyTotal = 3Arrangements = 3!Arrangements = 3*2*1 = 6Total Arrangements = 2 * 120 * 6Total Arrangements = 1440c. If the mathematics book must be together but other books can be arranged in any orderTo get the Number of Possible Arrangements First, Calculate the Possible Arrangements of Mathematics Books;Number of Mathematics Books = 2Arrangements = 2!Arrangements = 2*1 = 2Then Calculate the Possible Arrangements of the Mathematics book bundle with other books;The mathematics book bundled together is 1Other books = 5 Novels + 1 BiologyTotal = 7Arrangements = 7!Arrangements = 7*6*5*4*3*2*1Arrangements = 5040Total Possible Arrangements = 2 * 5040 = 10080 ways