Question

For a segment of a radio show , a disc jockey can play 7 records if there are 10 records to select from , in how many ways can the program for this segment be arranged

Answer 1

Total number of ways to play record 604,800

Explanation:

We have given the information:

A disc jockey can play 7 records and in total there are 10 records from where we can select.

we will use permutation in this since, we have to find the arrangement

Number of arrangements will be
`^(10)P_7`

Using
`^(n)P_r=(n!)/((n-r)!)`

And
`n!=n\cdot (n-1)\cdot (n-2).....\cdot 1`

Here n=10 and r=7

n is the total number of the thing to choose from and r is the number we have chosen from total.

`^(10)P_7=(10!)/((3)!)`

`\Rightarrow \frac{10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot3!} {3!}`

3! will get cancel from numerator and denominator.

`\Rightarrow \frac{10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4}`

`\Rightarrow 604800`