Using combinations, 15400 different groups of 3 books are available from the list of 12.
Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements.
Given
Total number of books = 12
You are to choose 3 books to read over the summer.
Number of different group of 3 books = [tex]\frac{12C_{3}.(9C_{3}).(6C_{3}).(3C_{3} ) }{4!}[/tex]
= [tex]\frac{\frac{12!}{3!9!} .\frac{9!}{3!6!} .\frac{6!}{3!3!} }{4!}[/tex]
= 15400.
Thus, 15400 different groups of 3 books are available from the list of 12.
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