Question 1092056: Student are given a list of nine books and told that they will be examined on the contents of five of them.How many combinations of five book are
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website! Question:
Student are given a list of nine books and told that they will be examined on the contents of five of them.How many combinations of five book are
Solution:
Imagine the teacher picks 5 books at random.
Her first book would be one out of 9,
the second book would be one out of 8,
...
the fifth book would be one out of 5, leaving four behind.
Therefore the number of permutations would be 9*8*7*6*5=15120
However, she could have chosen the same five books in many different orders, namely 5*4*3*2*1=120
Therefore, the total number of ways of picking 5 books out of nine, where order does not count, is 15120/120=126.
In general, the number of combinations of r objects taken from n objects is C(n,r)=n!/(r!(n-r)!)=9!/(5!4!)=126, same as above.
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