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# Counting

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I have \$3\$ different mathematics textbooks, \$2\$ different psychology textbooks, and \$2\$ different chemistry textbooks. In how many ways can I place the \$7\$ textbooks on a bookshelf, in a row, if all three mathematics textbooks must be together?

Jun 22, 2024

#1
+944
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I have \$3\$ different mathematics textbooks, \$2\$ different psychology textbooks, and \$2\$ different chemistry textbooks. In how many ways can I place the \$7\$ textbooks on a bookshelf, in a row, if all three mathematics textbooks must be together?

Temporarily consider the group of three math books as one unit.

Then, 1 group + 2 psych + 2 chem can arrange to 5P5 = 120 ways.

But wait.  You could arrange the three math books 6 different ways.

So all the possible arrangements is 120 • 6 = 720 ways.

.

Jun 22, 2024

#1
+944
+1

I have \$3\$ different mathematics textbooks, \$2\$ different psychology textbooks, and \$2\$ different chemistry textbooks. In how many ways can I place the \$7\$ textbooks on a bookshelf, in a row, if all three mathematics textbooks must be together?

Temporarily consider the group of three math books as one unit.

Then, 1 group + 2 psych + 2 chem can arrange to 5P5 = 120 ways.

But wait.  You could arrange the three math books 6 different ways.

So all the possible arrangements is 120 • 6 = 720 ways.

.

Bosco Jun 22, 2024