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A radio show plays the top 10 musical hits of the previous week. During the first full week of last January, these 10 hits were chosen from 70 possibilities, and they were played in order of increasing popularity. How many possible orders were there? Note: Since calculators cannot evaluate large factorials, use the approximation given by the formula .
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VerifiedWe have a radio that plays the top musical hits. We have to determine how many possible orders were there. These hits were chosen from possibilities, and they were played in order of increasing popularity. We have to determine how many possible orders were there.
When we use combinations instead of permutations?
Action 1.
First we choose 10 tracks out of 70, in no particular order.
The number of ways of doing this is Action 2.\ Arrange the 10 tracks in order of increasing popularity.\\ Once chosen, there is only {\bf one} arrangement of these tracks which represents the order by increasing popularity.\\
By the Multiplication Principle, the number of total arrangements , then, is \qquad \\${}{70}C{10}\cdot 1.
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